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Financial performance ranking of nationalized banks through integrated ahm-gra-dea method
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In this paper an effort is made to rank the some of public sector banks in India basing on their financial soundness. In this work AHM methodology is applied to determine weightages of CAMEL ratios and after obtaining weightages Grey Relation analysis is applied to get Grey Relation coefficient and then these two are applied in Data Envelop Analysis to obtain ranks.

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  1. International Journal of Management (IJM)
    Volume 10, Issue 3, May-June 2019, pp. 15-35, Article ID: IJM_10_03_003
    Available online at http://www.iaeme.com/ijm/issues.asp?JType=IJM&VType=10&IType=3
    Journal Impact Factor (2019): 9.6780 (Calculated by GISI) www.jifactor.com
    ISSN Print: 0976-6502 and ISSN Online: 0976-6510
    © IAEME Publication

    FINANCIAL PERFORMANCE RANKING OF
    NATIONALIZED BANKS THROUGH
    INTEGRATED AHM-GRA-DEA METHOD
    V.K. Viswanatha Raju
    Part-time Ph.D. Scholar in Department of Mechanical Engineering,
    College of Engineering (A), Andhra University, Visakhapatnam-3, India

    VVS Kesava Rao
    Professor, Department of Mechanical Engineering, College of Engineering (A)
    Andhra University, Visakhapatnam-3, India

    ABSTRACT
    In this paper an effort is made to rank the some of public sector banks in India
    basing on their financial soundness. In this work AHM methodology is applied to
    determine weightages of CAMEL ratios and after obtaining weightages Grey Relation
    analysis is applied to get Grey Relation coefficient and then these two are applied in
    Data Envelop Analysis to obtain ranks.
    Keywords: AHM, CAMEL ratios, GRA, DEA.
    Cite this Article: V.K. Viswanatha Raju and VVS Kesava Rao, Financial Performance
    Ranking of Nationalized Banks Through Integrated Ahm-Gra-Dea Method,
    International Journal of Management, 10 (3), 2019, pp. 15-35.
    http://www.iaeme.com/IJM/issues.asp?JType=IJM&VType=10&IType=3

    1. INTRODUCTION
    Performance evaluation of Banks is a major concern for the managers, shareholders, creditors,
    employees and customers, as strong banking system effects the growth and financial stability
    of the country. At the same time the banks must find a way to keep government regulators
    satisfied that their operating policies, loans, and investments are sound, protecting the public
    interest. The Indian banking sector has been the back bone of the Indian economy, helping it
    survives the various national and worldwide economic shocks and meltdowns.
    To measure the financial position of each bank and manage it efficiently and effectively so
    many efforts have been made from time to time. In the process of continuous evaluation of the
    bank’s financial performance the academicians, scholars and administrators have made several
    studies. However, with the Reserve Bank of India taking strong measures based on the
    recommendations of the Narasimhan committee, the land scope of Indian banking system
    changed together. All the banks were directed to follow the norms of capital adequacy, Asset
    quality, provisioning for Non-Performing Assets (NPAs), prudential norms, disclosure
    requirements, stream lining the processor’s and complain with accounting standards,

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  2. V.K. Viswanatha Raju and VVS Kesava Rao

    acceleration of pace and reach of latest technology and making financial statement transparent.
    Towards this end, they redefined their processes, methods, objectives, strategies, technologies
    and policies required to evaluate their financial position from period to period. For this purpose
    RBI suggested two supervisory rating models based on the recommendations made by
    Padmanabhan working group (1995) named CAMELS (Capital adequacy, Asset quality,
    Management capability, Earning quality, Liquidity and sensitivity), and CACS (Capital
    adequacy, Asset quality, Compliance, Systems and Control) for rating of Indian commercial
    banks and foreign banks operating in India . Further, different performance measurement tools
    and techniques have been developed in India as well as in other countries to evaluate the
    performance of banks. In performance evaluation of banking institutions, CAMEL rating is
    much popular among regulators due to its effectiveness in different countries including India.
    The CAMEL Criteria and the sub-criteria under each criterion is discussed below.

    2. CAMEL CRITERIA
    The performance of banks, both public and private, has been analyzed by academicians,
    scholars and administrators using CAMEL model in the last decade. The performance
    dimensions under CAMEL approach are Capital Adequacy (CA), Asset Quality (AQ),
    Management Efficiency (ME), Earning Quality (EQ) and Liquidity (LI) are considered in the
    study. Performance dimensions and their enables are briefly explained below.

    2.1. Capital Adequacy (CA)
    Capital base of financial institutions facilitates depositors in forming their risk perception about
    the organization. Also, it is important for financial managers to maintain adequate levels of
    capitalization. Capital adequacy is very useful for a bank to conserve & protect stakeholders‟
    confidence and prevent the bank from bankruptcy. For the study, the following ratios have been
    used to measure capital adequacy:
    Capital adequacy ratio: Capital adequacy ratios (“CAR”) are a measure of the amount of a
    bank’s core capital expressed as a percentage of its risk-weighted asset. The capital adequacy
    ratio is developed to ensure that banks can absorb a reasonable level of losses occurred due to
    operational losses and determine the capacity of the bank in meeting the losses. As per the latest
    RBI norms, the banks should have a CAR of 9 per cent.
    Advance to Assets Ratio (Advances/Assets): This is the ratio indicates a bank’s
    aggressiveness in lending which ultimately results in better profitability.
    Government Securities to Total Investments (G-sec/Investments): It is an important
    indicator showing the risk-taking ability of the bank. It is a bank’s strategy to have high profits,
    high risk or low profits, low risk.

    2.2. Asset Quality (AQ)
    Asset quality determines the healthiness of financial institutions against loss of value in the
    assets as asset impairment risks the solvency of the financial institutions. The weakening value
    of assets has a spillover effect, as losses are eventually written-off against capital, which
    eventually expose the earning capacity of the institution. With this framework, the asset quality
    is assessed with respect to the level and severity of non-performing assets, adequacy of
    provisions, distribution of assets etc. For the study, the following ratios have been used to
    measure asset quality:
    Net NPAs to Net Advances (NNPAs/NA): It is the most standard measure of assets quality
    measuring the net non-performing assets as a percentage to net advances.
    Net NPAs to Total Assets (NNPAs/TA): This ratio discloses the efficiency of bank in
    assessing the credit risk and, to an extent, recovering the debts.

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  3. Financial Performance Ranking of Nationalized Banks Through Integrated Ahm-Gra-Dea Method

    Total Investments to Total Assets (TI/TA): It indicates the extent of deployment of assets in
    investment as against advances.

    2.3. Management Efficiency (ME)
    Management efficiency, another indispensable component of the CAMEL framework, means
    adherence to set norms, knack to plan and be proactive in the dynamic environment, leadership,
    innovativeness and administrative competence of the bank. The following ratios have been used
    to measure management efficiency.
    Business per Employee: Business per employee shows the productivity of human force of
    bank. It is used as a tool to measure the efficiency of employees of a bank in generating business
    for the bank.
    Profit per Employee: This shows the surplus earned per employee. It is known by dividing
    the profit after tax earned by the bank by the total number of employees.
    Credit deposit ratio (ME3): It is the ratio of the total advances to deposits. It indicates the
    ability of a bank to convert its deposits into higher earning advances.

    2.4. Earning Quality (EQ)
    The quality of earnings represents the sustainability and growth of future earnings, value of a
    bank’s lucrativeness and its competency to maintain quality and earn consistently. Earnings and
    profitability are examined as against interest rate policies and adequacy of provisioning. The
    single best indicator used to gauge earning is the Return on Assets (ROA), which is net income
    after taxes to total asset ratio. For the study, the following ratios have been used to measure
    earnings quality.
    Return on assets: It is the ratio of Income to the assets. This ratio expresses the quality of
    income in form of income generated by core activities income.
    NIM to total assets: NIM is the difference between the interest income and the interest
    expended. It is expressed as a percentage of total assets. A higher spread indicates better
    earnings, given the total assets.
    Operating Profit to Total Assets Ratio (OPP/TA): This ratio indicates how much profit a
    bank can earn from its operations for every rupee invested in its total assets. It is the ratio
    between operating profits to total assets.
    Interest income to total income: It is the ratio between interest incomes to total income.

    2.5. Liquidity (LI)
    In case of an adequate liquidity position, the institution can obtain sufficient funds, either by
    increasing liabilities or by converting its assets to cash quickly at a reasonable cost. The
    following ratios have been used to measure liquidity:
    Liquid Assets to Total Assets (LA/TA): It measures the overall liquidity position of the bank.
    The liquid asset includes cash in hand, balance with institutions and money at call and short
    notice. The total assets include the revaluation of all the assets.
    G-Sec to Total Assets (G-Sec/TA): It measures the risk involved in the assets. This ratio
    measures the Government securities as proportionate to total assets.
    Liquid Assets to Total Deposits (LA/TD): This ratio measures the liquidity available to the
    total deposits of the bank.
    Liquid Assets to Demand Deposits (LA/DD): This ratio measures the ability of bank to meet
    the demand from depositors in a particular year. To offer higher liquidity for them, bank has to
    invest these funds in highly liquid form.

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  4. V.K. Viswanatha Raju and VVS Kesava Rao

    3. LITERATURE SURVEY
    Akbar Alem Tabriz, et al. (2014) [1] considered Fuzzy AHP and TOPSIS to accomplish, the
    more ideal level of performance evaluation and to reveal the ranking of branches and identify
    the ones taking leading positions in the market. In the study, financial ratios namely: Cash flow,
    return on assets, capital adequacy ratio, and demanding loss ratios are considered.
    Zeliha Kaygisiz Ertuğ, et al. (2015) [2] developed an evaluation model that considers the
    quantitative and qualitative criteria for the appropriate selection of firms demanding
    commercial credit for both public and private banks. In this paper, the authors proposed an
    integrated model that combines the AHP and GRA into a single evaluation model. The model
    is illustrated with a case study.
    Elham Shadkam, et al. (2015) [3] considered DEA, RSM and Cuckoo algorithm and
    presented a combinatory algorithm called DRC in which one response surface function for
    efficiency is obtained instead of a multi-response surface functions for each response. The
    proposed approach has been verified by using data from 40 active branches of Refah bank in
    Mashhad.
    Dariush Akbarian (2015) [4] adopted cross efficiency and analytic hierarchy process (AHP)
    methods to evaluate the performance of 20 branch banks of Iran. In the first stage the cross-
    efficiency value of each DMU is specified. In the second stage, the pairwise comparison matrix
    generated in the first stage is utilized to rank the scale of the units via the one-step process of
    AHP.
    Mousa. G. A (2015) [5] examined the efficiency of the banking sector in the Bahrain Bourse
    using financial ratio analysis (FRA) and DEA. For FRA, the current study has used six ratios
    to evaluate three characteristics of banks’ efficiency (Profitability; Liquidity and Risk). The
    findings have revealed that 2 banks are fully efficient in the period from 2009-10 to 2012-13).
    Arora, et al. (2015) [6] made a study to find the performance of public banks in Turkey,
    from FYs 2004-05 to 2013-14, through an integrated model combining the AHP and the
    Operational Competitiveness Rating method (OCRA). The input and output weights were
    calculated by AHP while the efficiency of the banks was measured by OCRA.
    Mehmet Ozcalici, et al. (2015) [7] adopted TOPSIS, fuzzy TOPSIS and GRA to forecast
    the rankings of return on the asset of the Turkish banking sector by utilizing dataset on financial
    indicators for the FY 2013-14.
    Asmita Chitnis, et al. (2016) [8] proposed a unified approach based on DEA and TOPSIS
    to overcome the difficulty of unique ranking in the prevalent benchmarking and performance
    evaluation processes. The authors presented a case of an Indian bank to illustrate an application
    of the proposed approach.
    Mohammad, et al. (2016) [9] identified the criteria and their coefficients used for financial
    performance evaluation of private banks using the fuzzy AHP method. After that, the authors
    evaluated financial performance of Iran private banks and ranked them using the information
    on the financial statements through TOPSIS method
    Mehdi Fallah Jelodar (2016) [10] prioritized the factors affecting performance efficiency in
    the areas of management, personnel, finance, and customers using the methods of DEA and
    hierarchical analysis.
    There are number of multi-criteria decision-making approaches like AHP, ANP,
    DEMATEL, TOPSIS etc are available in the literature are useful to evaluate the performance
    of banks. In the recent past, integrated approaches or hybrid models (SCOR-BSC, BSC-AHP,
    BSC-ISM-ANP, DEA – AHP model, Fuzzy AHP- Fuzzy TOPSIS, BSC-ANP-DEMATEL,
    Delphi method-AHP-TOPSIS, Dependence-based interval-valued ER (DIER)-BSC,

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  5. Financial Performance Ranking of Nationalized Banks Through Integrated Ahm-Gra-Dea Method

    DEMATEL- ANP- VIKOR) have also been proposed for performance measurement and
    analysis.
    Data from 20 banks for a period of five years is collected and applied in the analysis.

    4. METHODOLOGY
    In the proposed method the relative weights of CAMEL criteria and their sub-criteria are
    obtained through AHM. Then the financial soundness of banks is evaluated and analyzed
    through integrated method of AHM-GRA-DEA method.
    The methodology is explained in the following manner.
    The AHM method is discussed below.

    4.1. The steps of AHM:
    Step-4.1: Though, CAMEL rating is much popular among regulators due to its effectiveness in
    different countries including India, this method could not import the weights to the performance
    dimensions/enablers to evaluate the financial soundness of Banks. In lieu of this, the relative
    weights of performance dimensions and their enablers need to be considered to evaluate the
    financial soundness of public sector banks.
    In AHM, related matrix of attribute measures (ij) are determined from pair wise
    comparison matrix A = (aij) of AHP using the conversion equation as shown below.

     k
     k  1 aij  k , aij  1

     1 1
     ij   aij  , aij  1
    k  1 k

    0.5 aij  1, i  j

    0 aij  1, i  j
    Relative attribute weight of the jth criterion (Wcj) is obtained from the following relation.
    J
    2
    Wc j  *   ij
    J * ( j  1) i 1 j = 1,2,…,J
    Wc = [Wc1, Wc2, …, WcJ] Step-4.2: Determining Grey Relational coefficient for entire 17 CAMEL ingredients for
    each bank.

    4.2. Grey Relation Analysis
    Grey relational analysis is a kind of method which enables determination of the relational
    degree of every factor in the system. The method can be used for systems that are incompletely
    described with relatively few data available, and for which standard statistical assumptions are
    not satisfied. Grey relation analysis quantifies all influences of various factors and their
    relations. It uses information from the Grey system to dynamically compare each factor
    quantitatively, based on the level of similarity and variability among factors to establish their
    relation. GRA analyzes the relational grade for discrete sequences. Let the number of
    the banks be m, and the number of the influence factors be n. Then a m × n value matrix is set
    up as shown in equation.

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  6. V.K. Viswanatha Raju and VVS Kesava Rao

     x1 (1), x1 (2),….. x1 (n) 
     x (1), x (2),…. x (n) 
     2 2 2 
    …. 
     
    …. 
     xm (1), xm (2),…. xm (n)
    X=  
    where xi(j) is the value of j influence factors of ith bank.
    th

    Step-4.2.1: Determination of Influence factors for each CAMEL ingredients.
    Usually, two kinds of influence factors are included, they are:
    1. Benefit – type factor (the bigger the better),
    2. Cost – type (the smaller the better)
    Benefit type:
    xi ( j )  min xi ( j )
    xsi ( j ) 
    max xi ( j )  min x( j ) (1)
    Cost type:
    min xi ( j )  xi ( j )
    xsi ( j ) 
    max xi ( j )  min x( j ) (2)
    th th
    where xi(j) is the reference value of j enabler of i bank.
    For evaluating the financial performance 17 ratios are considered.
    For normalizing banking financial ratios 1,2,3,7,8,9,10,11,12,13,14,15,16,17 benefit type
    Eq.(1) is applied.
    For normalizing banking financial ratios 4,5,6 cost type Eq.(2) is used.
    Step-4.2.2: Determine absolute differences
    The absolute difference in the compared series and the referential series should be obtained
    by using the following equation.
    xi(j) = |x0(j) – xsi(j)|
    x0(j) = reference value of j enabler of ith bank.
    th

    Step-4.2.3: Find out the maximum and minimum absolute differences.
    The maximum (max) and the minimum (min) difference should be found from the
    absolute difference of the compared series and the referential series.
    Step-4.2.4: Determine grey relation coefficient
    In Grey relational analysis, Grey relational coefficient  can be expressed as shown in
    equation
     min  p max
    i ( j ) 
    xi ( j )  p max
    The distinguishing coefficient p is between 0 and 1. Generally, the distinguishing
    coefficient p is set to 0.5.

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  7. Financial Performance Ranking of Nationalized Banks Through Integrated Ahm-Gra-Dea Method

    Step-4.3: Using DEA based method determine ranking of the each bank.

    4.3. DEA Based GRA Model
    Data envelopment analysis, first proposed by Charnes, Cooper and Rhodes in 1978, based on
    the earlier work started by Farrell (1957) and developed by Banker (1984), is a mathematical
    technique developed in operations research and management science for measuring productive
    efficiency. The basic models of DEA are CCR (Charnes, Cooper, and Rhodes) BCC (Banker,
    Charnes and Cooper) additive and SBM.
    Optimistic and pessimistic additive DEA models:
    As all the grey relational coefficients are benefit (output) data, an optimistic additive DEA
    model for obtaining attribute weights in GRA can be developed like the additive model in
    Cooper et al (1999) without explicit inputs as follows:
    n
    Pk  max  e j s j
    j 1

    n

     
    j 1
    i ij  s j   kj j
    s.t. (3)
    m

    i 1
    i 1

    s j ,  i  0
    where 1 – Pk indicates the grey relational grade, h(k = 1,2,m), for alternative under

    assessment Ak (known as a DMU in the DEA terminology) and 0  Pk  1. s j is the slack
    variable of attribute Cj(j = 1,2,…,n), expressing the difference between the performance of a
    composite alternative and the performance of the assessed alternative with respect to each

    attribute. In other words, s j identifies a shortfall in the attribute value of Cj for alternative Ak
    Obviously, when Pk = 0 alternative Ak is considered as the best alternative in comparison to all
    the other alternatives, ej is the priority weight of attribute Cj which is defined out of the internal
    mechanism of frontier for an additive model. The dual of equation (3) can be developed as
    follows:
    n
    k  max  w j  kj  w0
    j 1

    n

    w 
    j 1
    j ij  w0  1i
    s.t. (4)

    wj  ej j
    w0 free
    This model is useful for our purpose in dealing with grey relational grades. The objective
    function in equation (4) maximizes the ratio of the grey relational grade of alternative Ak to the
    maximum grey relational grade across all alternatives for the same set of weights (max k/max
    i), while the priority weights obtained by AHP impose the lower bounds on the attribute
    weights. Hence, an optimal set of weights in model priori information about the priorities of

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  8. V.K. Viswanatha Raju and VVS Kesava Rao

    attributes, simultaneously. Finally, one should notice that the optimistic additive DEA models
    bounded by AHP does not necessarily yield results that are different from those obtained from
    the original additive DEA models (Charnes et al, 1985). In particular, it does not increase the
    power of discrimination between the considerable number of alternatives, which are usually
    ranked in the first place by obtaining the grey relational grades of 1. To overcome these issues,
    we develop the additive models from the pessimistic point of view in which each alternative is
    assessed based on its distance from the worst practice frontier as follows:
    n
    Pk  max  e j s j
    j 1

    m

      
    i 1
    i ij  s j   kj j
    s.t. (5)
    m

       1
    i 1
    i

    s j , i  0
    Note that the only difference between equation (3) and equation (5) is the signs of slack
    variables in the first set of constraint, sf is the slack variable of attribute Cfj = 1,2,…,«),
    expressing the difference between the performance of the assessed alternative and the
    performance of a composite alternative with respect to each attribute. The dual model of
    equation (5) is shown below.
    n
    k  max  wj  kj  w0
    j 1

    n

     w 
    j 1
    j ij  w0  1i
    s.t. (6)

    wj  e j j

    w0 free.
    Here, we seek the worst weights in the sense that the objective function in equation (6) is
    minimized. The first set of constraints assures that the computed weights do not attain a grade
    smaller than 1. Each alternative is compared with these worst alternatives and is assessed based
    on the ratio of the distance from the worst-practice frontier. It is worth pointing out that the
    pessimistic additive models in this paper are not brand-new models in the DEA literature.
    Conceptually, it is parallel to the additive DEA models as discussed by Jahanshahloo and
    Afzalinejad (2006) for ranking alternatives on a full inefficient-frontier.
    To combine the grey relational grades obtained equation (4) and (6), that is the best and
    worst sets of weights, the linear combination of corresponding normalized grades is
    recommended as follows (Zhou et al., 2007):
    k  min   min

     k ()    (1  ) k
    max  min   min
    max 
    (7)

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  9. Financial Performance Ranking of Nationalized Banks Through Integrated Ahm-Gra-Dea Method

    where max = max{k, k = 1,2,…,m},min = min{k, k = 1,2,…,m}, max  = max{ k , k =
     = min{ k , k = 1,2,…,m} and 0    1 is an adjusting parameter, which may
    1,2,…,m}, { min
    reflect the preference of a decision-maker on the best and worst sets of weights. k() is a
    normalized compromise grade in the range [0, 1].
    Step-4.4: Determine Ranking of Banks
    Banks are ranked basing on the descending order of normalized grey relation grade.

    5. MODEL CALCULATION FOR INTEGRATED AHM-GRA-DEA
    The banks are ranked for the five financial years based on integrated AHM-GRA-DEA method.
    The data shown in the Table-16 for the 1st financial year is considered to evaluate the financial
    soundness. The model calculations are presented for the 1st financial year.

    5.1. Relative weights of CAMEL criteria
    Relative weights of criteria are determined through AHM using pair wise comparison matrix.
    The pair-wise comparison is performed on the basis of how an element dominates the other and
    the judgments are entered using Saaty’s 1–9 scale. The decision maker can express his
    preference between each pair of elements verbally as equally important, moderately more
    important, strongly more important, very strongly more important, and extremely more
    important. These descriptive preferences would then be translated into numerical values 1, 3,
    5, 7, 9, respectively, with 2, 4, 6, and 8 as intermediate values for comparisons between two
    successive judgments. Reciprocals of these values are used for the corresponding transposed
    judgments. Table-1 shows the comparison scale used by Saaty.

    Table 1 Pair wise comparison scale (Saaty scale)
    Intensity of
    Definition Explanation
    Importance
    1 Equal importance Two activities contribute equally to the objective
    Experience and judgment slightly favour one activity over
    3 Moderate importance
    another
    Experience and judgment very strongly over another, its
    5 Strong importance
    dominance demonstrated in practice
    An activity is favoured very strongly over another,
    7 Very strong importance
    its dominance demonstrated in practice
    The evidence favouring one activity over another is
    9 Extreme importance
    of the highest possible order of affirmation
    Sometimes one needs to interpolate a compromise
    For compromise between the
    2,4,6,8 judgment numerically because there is no good word to
    above values
    describe it
    Pair wise comparison matrix of criteria is formulated by the discussions with the process
    experts of the organization. Pair wise comparison matrix of CAMEL parameters is obtained as
    shown below.

    Table 2 Pair wise comparison matrix
    CA AQ ME EQ LI
    CA 1.0000 0.1429 0.1111 0.2000 0.3333
    AQ 7.0000 1.0000 0.3333 3.0000 5.0000
    ME 9.0000 3.0000 1.0000 5.0000 7.0000
    EQ 5.0000 0.3333 0.2000 1.0000 3.0000
    LI 3.0000 0.2000 0.1429 0.3333 1.0000

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  10. V.K. Viswanatha Raju and VVS Kesava Rao

    Comparison judgement matrix
     k
     k  1 aij  k , aij  1

     1 1
     ij   aij  , aij  1
    k  1 k

    0.5 aij  1, i  j

    0 aij  1, i  j

    Model calculation:
    For i =, j = 1; aij = 1.00; Then ij = 0.000;
    k
    For i = 2, j = 1; aij = k = 7.00 (>1); Then ij = ;
    k  1
    So ij = (2 * 7.00)/(2 * 7.00 + 1) = 14/15 = 0.9333;
    k
    For i = 1, j = 3; aij = 1/k = 0.1111 (

  11. Financial Performance Ranking of Nationalized Banks Through Integrated Ahm-Gra-Dea Method

    These priority values of the performance dimensions form a basis for steps to improve the
    performance of the banks in terms of soundness. In the study, the respondents show high
    relative importance to Management soundness which is a key to judge the decision making
    capacity of managing board of banks.

    5.2. Relative weights of sub criteria under each CAMEL criterion

    5.2.1. Capital Adequacy
    Pair wise comparison matrix of sub criteria of capital adequacy is formulated by the discussions
    with the process experts of the organization. Pair wise comparison matrix of capital adequacy
    sub-criteria is obtained as shown below.

    Table 5 Sub criteria for capital adequacy
    Capital Adequacy CA1 CA2 CA3
    CA1 1 5 7
    CA2 1/5 1 5
    CA3 1/7 1/5 1

    Table 6 Final capital adequacy sub criteria weights
    Capital Adequacy CA1 CA2 CA3
    Relative weights 0.6141 0.3333 0.0526

    5.2.2. Asset Quality
    Pair wise comparison matrix of sub criteria of Asset Quality is formulated by the discussions
    with the process experts of the organization. Pair wise comparison matrix of capital adequacy
    sub-criteria is obtained as shown below.

    Table 7 Sub criteria for asset quality
    Asset Quality AQ1 AQ2 AQ3
    AQ1 1 2 3
    AQ2 1/2 1 2
    AQ3 1/3 1/2 1
    Relative weights of Capital adequacy sub-criteria criteria are obtained through AHM
    method using pair wise comparison matrix of criteria and are shown in the following Table-8.

    Table 8 Final asset quality sub criteria weights
    Asset Quality AQ1 AQ2 AQ3
    Relative weights 0.5524 0.3333 0.1143

    5.2.3. Management Efficiency
    Pair wise comparison matrix of sub criteria of management efficiency is formulated by the
    discussions with the process experts of the organization. Pair wise comparison matrix of capital
    adequacy sub-criteria is obtained as shown below.

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  12. V.K. Viswanatha Raju and VVS Kesava Rao

    Table 9 Sub criteria for management efficiency
    Management Efficiency ME1 ME2 ME3
    ME1 1 2 4
    ME2 1/2 1 3
    ME3 1/4 1/3 1
    Relative weights of management efficiency sub-criteria criteria are obtained through AHM
    method using pair wise comparison matrix of criteria and are shown in the following Table-10.

    Table 10 Final management efficiency sub criteria weights
    Management Efficiency ME1 ME2 ME3
    Relative weights 0.5630 0.3524 0.0846

    5.2.4. Earning Qualit:
    Pair wise comparison matrix of sub criteria of earning quality is formulated by the discussions
    with the process experts of the organization. Pair wise comparison matrix of earning quality
    sub-criteria is obtained as shown below.

    Table 11 Sub criteria for earning quality
    Earning Quality EQ1 EQ2 EQ3 EQ4
    EQ1 1 3 4 6
    EQ2 1/3 1 3 4
    EQ3 1/4 1/3 1 3
    EQ4 1/6 1/4 1/3 1
    Relative weights of earning quality sub-criteria criteria are obtained through AHM method
    using pair wise comparison matrix of criteria and are shown in the following Table-12.

    Table 12 Final earning quality sub criteria weights
    Earning Quality EQ1 EQ2 EQ3 EQ4
    Relative weights 0.4448 0.3148 0.1852 0.0552

    5.2.5. Liquidity
    Pair wise comparison matrix of sub criteria of liquidity is formulated by the discussions with
    the process experts of the organization. Pair wise comparison matrix of earning quality sub-
    criteria is obtained as shown below.

    Table 13 Sub criteria for liquidity
    Liquidity LI1 LI2 LI3 LI4
    LI1 1 5 7 9
    LI2 1/5 1 6 8
    LI3 1/7 1/6 1 6
    LI4 1/9 1/8 1/6 1
    Relative weights of liquidity sub-criteria criteria are obtained through AHM method using
    pair wise comparison matrix of criteria and are shown in the following Table-14.

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  13. Financial Performance Ranking of Nationalized Banks Through Integrated Ahm-Gra-Dea Method

    Table 14 Final liquidity sub criteria weights
    Liquidity LI1 LI2 LI3 LI4
    Relative weights 0.4650 0.3259 0.1777 0.0314
    Global weights of the performance enablers are determined by multiplying the relative
    weight of the performance enabler with the weight of the respective dimension. Global weights
    of the performance enablers are shown in Table-15.

    Table 15 Global weights of performance enablers
    Performance Global
    Weight Performance Enabler Weight
    Dimension Weight
    Capital adequacy ratio 0.6141 0.0217
    Capital Adequacy
    0.0353 Advances to assets 0.3333 0.0118
    (CA)
    Government securities to total investments 0.0525 0.0019
    Net NPA to Net Advance 0.5524 0.1570
    Asset Quality
    0.2842 Net NPA to Total Assets 0.3333 0.0947
    (AQ)
    Total Investments to Total Assets 0.1143 0.0325
    Management Business per employee 0.5630 0.2053
    Soundness 0.3647 Profit per employee 0.3524 0.1285
    (MS) Credit deposit ratio 0.0847 0.0309
    Return on assets 0.4449 0.0890
    Earning Quality NIM to total assets 0.3148 0.0630
    0.2000
    (EQ) Operating profit to total assets 0.1852 0.0370
    Interest income to total income 0.0551 0.0110
    Liquid assets to total assets 0.4650 0.0538
    Liability Government securities to total assets 0.3259 0.0377
    0.1158
    (LI) Liquid assets to total deposits 0.1778 0.0206
    Liquid assets to demand deposits 0.0314 0.0036

    5.3. Data on financial ratios
    The data on the financial ratios of the banks is obtained through annual reports, financial
    statements etc.

    Table 16 Data on financial ratios for the 1st financial year
    Capital Management
    Asset Quality Earning Quality Liquidity
    Banks Adequacy Efficiency
    CA1 CA2 CA3 AQ1 AQ2 AQ3 ME1 ME2 ME3 EQ1 EQ2 EQ3 EQ4 LI1 LI2 LI3
    Bank l 12.96 61.89 81.25 0.79 0.49 28.59 10.63 6.70 70.99 1.11 2.23 2.02 88.93 5.22 23.23 5.99
    Bank 2 14.38 65.60 93.87 0.38 0.25 22.23 11.65 9.00 77.52 1.36 2.95 2.22 90.24 6.60 20.86 7.80
    Bank 3 14.52 63.81 83.23 0.35 0.22 19.92 12.29 11.00 74.87 1.33 0.87 1.95 88.62 5.54 16.58 6.50
    Bank 4 12.17 60.68 80.71 0.91 0.55 24.45 12.84 6.20 71.30 0.82 0.54 1.53 89.17 6.20 24.78 7.29
    Bank 5 13.35 61.33 82.44 1.32 0.81 29.42 8.25 2.38 70.13 0.47 3.69 1.12 91.29 5.03 24.26 5.75
    Bank 6 15.38 62.89 85.07 1.10 0.69 24.90 11.99 9.76 72.00 1.42 0.93 1.81 89.08 6.55 21.18 7.50
    Bank 7 11.64 61.85 87.62 0.65 0.40 25.98 8.35 3.96 72.33 0.70 1.58 1.24 92.33 6.71 22.77 7.85
    Bank 8 14.11 60.52 64.65 0.46 0.28 30.28 15.73 10.92 74.39 1.21 1.99 1.78 87.91 5.67 19.57 6.97
    Bank 9 13.64 62.00 79.12 1.06 0.66 26.94 23.46 11.93 87.04 0.73 8.29 1.64 89.64 7.72 21.32 10.84
    Bank 10 13.56 61.82 75.67 0.53 0.33 28.58 9.30 8.88 71.12 1.53 3.08 2.70 88.79 5.65 21.62 6.50

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  14. V.K. Viswanatha Raju and VVS Kesava Rao

    Capital Management
    Asset Quality Earning Quality Liquidity
    Banks Adequacy Efficiency
    CA1 CA2 CA3 AQ1 AQ2 AQ3 ME1 ME2 ME3 EQ1 EQ2 EQ3 EQ4 LI1 LI2 LI3
    Bank 11 14.55 62.55 98.17 1.19 0.74 27.19 10.05 4.16 77.00 0.71 1.74 1.60 90.81 5.60 26.69 6.89
    Bank 12 14.23 59.44 73.87 0.98 0.58 30.71 14.18 9.04 68.97 1.03 1.65 2.01 92.64 5.90 22.68 6.84
    Bank 13 12.42 63.99 83.54 0.85 0.54 25.15 10.18 8.35 77.38 1.34 1.05 2.39 88.19 6.28 21.01 7.60
    Bank 14 11.68 65.45 97.16 0.83 0.54 21.48 7.51 5.00 76.52 0.96 5.37 1.81 88.23 8.54 20.87 9.98
    Bank 15 11.98 61.84 78.82 1.63 1.01 24.16 7.04 3.84 81.03 0.71 2.71 2.07 83.72 17.30 42.69 22.66
    Bank 16 12.54 64.87 80.11 0.98 0.64 25.26 8.88 8.00 79.17 1.12 3.66 1.66 90.00 6.64 20.23 8.10
    Bank 17 13.04 68.21 86.41 0.97 0.66 22.40 8.75 3.99 78.75 0.76 2.17 1.76 92.60 6.67 19.36 7.70
    Bank 18 13.71 60.63 83.69 1.84 1.12 26.27 10.69 4.19 68.19 0.66 1.88 1.65 92.47 6.37 29.01 7.16
    Bank 19 12.95 63.98 79.57 1.19 0.76 24.75 10.43 8.00 74.58 1.05 1.41 1.82 88.97 7.46 22.37 8.70
    Bank 20 13.05 59.42 72.83 1.42 0.84 29.16 8.60 3.48 68.73 0.66 3.54 1.67 90.87 6.60 21.24 7.63

    5.4. Normalized financial ratios
    Normalized Financial Ratios of the banks for the 1st financial Year are calculated as discussed
    in methodology and are shown in the Table-17.

    Model calculation:
    For example for bank 1 and CA1:
    CA1 is benefit criteria hence the following formula as discussed
    | xi ( j )  min xi ( j ) |
    xsi ( j ) 
    max xi ( j )  min x( j )
    Min of CA1 = 11.64; Max of CA1 = 15.38; CA1 of bank 1 = 12.96
    | 12.96  11.64 |
    = = 0.3529
    15.38  11.64
    For example for bank 2 and AQ1:
    AQ1 is cost criteria hence the following formula as discussed
    max xi ( j )  xi ( j )
    xsi ( j ) 
    max xi ( j )  min x( j )
    Min of AQ1 = 0.35; Max of AQ1 = 1.84; AQ1 of bank 2 = 0.38
    | 1.84  0.38 |
    = = 0.9799
    1.84  0.38
    Similarly, other values are calculated and shown in Table-17.
    Table-17: Normalized financial ratios (1st financial year)
    CA AQ ME HQ LI
    Banks
    CA1 CA2 CA3 AQ1 AQ2 AQ3 ME1 ME2 ME3 EQ1 EQ2 EQ3 EQ4 LI1 LI2 LI3 LI4
    Bank 1 0.3529 0.2804 0.4954 0.7047 0.7030 0.1967 0.2186 0.4524 0.1483 0.6038 0.2186 0.5679 0.5844 0.0156 0.2545 0.0140 0.0199
    Bank 2 0.7326 0.7023 0.8717 0.9799 0.9658 0.7863 0.2808 0.6932 0.4946 0.8396 0.3106 0.6920 0.7305 0.1277 0.1640 0.1208 0.4131
    Bank 3 0.7701 0.4986 0.5544 1.0000 1.0000 1.0000 0.3197 0.9026 0.3541 0.8113 0.0425 0.5231 0.5496 0.0418 0.0000 0.0444 0.2725
    Bank 4 0.1417 0.1434 0.4793 0.6242 0.6281 0.5799 0.3532 0.4000 0.1646 0.3302 0.0000 0.2615 0.6108 0.0955 0.3141 0.0907 0.6930
    Bank 5 0.4572 0.2170 0.5308 0.3488 0.3426 0.1192 0.0737 0.0000 0.1029 0.0000 0.4064 0.0000 0.8483 0.0000 0.2939 0.0000 0.0040
    Bank 6 1.0000 0.3943 0.6093 0.4948 0.4722 0.5388 0.3015 0.7728 0.2018 0.8962 0.0500 0.4381 0.6009 0.1241 0.1761 0.1034 0.3112
    Bank 7 0.0000 0.2758 0.6854 0.7987 0.7956 0.4379 0.0798 0.1654 0.2194 0.2170 0.1339 0.0737 0.9646 0.1371 0.2370 0.1240 0.3248
    Bank 9 0.6604 0.1250 0.0000 0.9262 0.9370 0.0398 0.5292 0.8942 0.3288 0.6981 0.1865 0.4169 0.4699 0.0524 0.1146 0.0722 0.0000

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  15. Financial Performance Ranking of Nationalized Banks Through Integrated Ahm-Gra-Dea Method

    CA AQ ME HQ LI
    Banks
    CA1 CA2 CA3 AQ1 AQ2 AQ3 ME1 ME2 ME3 EQ1 EQ2 EQ3 EQ4 LI1 LI2 LI3 LI4
    Bank 9 0.5348 0.2935 0.4319 0.5235 0.5072 0.3490 1.0000 1.0000 1.0000 0.2453 1.0000 0.3294 0.6633 0.2192 0.1815 0.3006 0.2385
    Bank 10 0.5134 0.2732 0.3288 0.8792 0.8822 0.1975 0.1376 0.6806 0.1553 1.0000 0.3278 1.0000 0.5681 0.0505 0.1931 0.0442 0.4761
    Bank 11 0.7781 0.3561 1.0000 0.4362 0.4170 0.3262 0.1833 0.1864 0.4675 0.2264 0.1547 0.3036 0.7943 0.0463 0.3872 0.0674 0.2620
    Bank 12 0.6925 0.0026 02752 0.5772 0.5973 0.0000 0.4348 0.6974 0.0413 0.5283 0.1430 0.5630 1.0000 0.0706 0.2338 0.0644 0.4220
    Bank 13 0.2086 0.5201 0.5637 0.6644 0.6449 0.5149 0.1911 0.6251 0.4871 0.8208 0.0653 0.8041 0.5013 0.1022 0.1698 0.1091 0.2989
    Bank 14 0.0107 0.6862 0.9700 0.6779 0.6411 0.8558 0.0286 0.2743 0.4416 0.4623 0.6232 0.4368 0.5056 0.2861 0.1642 02502 0.8980
    Bank 15 0.0909 0.2748 0.4227 0.1409 0.1202 0.6074 0.0000 0.1529 0.6808 0.2264 0.2804 0.6002 0.0000 1.0000 1.0000 1.0000 0.1370
    Bank 16 0.2406 0.6200 0.4613 0.5772 0.5371 0.5053 0.1121 0.5885 0.5824 0.6132 0.4030 0.3394 0.7033 0.1308 0.1399 0.1386 1.0000
    Bank 17 0.3743 1.0000 0.6493 0.5839 0.5113 0.7700 0.1041 0.1686 0.5601 0.2736 0.2105 0.4024 0.9953 0.1337 0.1064 0.1152 0.3831
    Bank 18 0.5535 0.1377 0.5681 0.0000 0.0000 0.4113 0.2223 0.1895 0.0000 0.1792 0.1727 0.3347 0.9812 0.1089 0.4760 0.0832 0.7561
    Bank 19 0.3503 0.5186 0.4453 0.4362 0.3933 0.5526 0.2065 0.5885 0.3386 0.5472 0.1123 0.4450 0.5888 0.1982 0.2217 0.1741 0.3103
    Bank 20 0.3770 0.0000 02440 0.2819 0.3074 0.1432 0.0950 0.1152 0.0284 0.1792 0.3875 0.3501 0.8015 0.1279 0.1784 0.1112 0.1150

    Absolute differences
    The absolute difference in the compared series and the referential series should be obtained by
    using equation as discussed.

    Model calculation:
    For bank 2 CA1
    The absolute difference in the compared series and the referential series is obtained using
    the following equation as discussed.
    xi(j) = |x0(j) – xsi(j)|
    Reference series = x0(j) = 1.0; xsi(j) = 0.7326 (from normalized data matrix)
    xi(j) = |1.000 – 0.7326| = 0.2674
    Similarly other values are calculated and the absolute differences are shown in Table-18.

    Table 18 Absolute differences for the 1st financial year
    CA AQ ME EQ LI
    Bank
    CA1 CA2 CA3 AQ1 AQ2 AQ3 ME1 ME2 ME3 EQ1 EQ2 EQ3 EQ4 LI1 LI2 LI3 LI4
    Bank 1 0.6471 0.7196 0.5046 0.2953 0.2970 0.8033 0.7814 0.5476 0.8517 0.3962 0.7814 0.4321 0.4156 0.9844 0.7455 0.9860 0.9801
    Bank 2 0.2674 0.2977 0.1283 0.0201 0.0342 0.2137 0.7192 0.3068 0.5054 0.1604 0.6894 0.3080 0.2695 0.8723 0.8360 0.8792 0.5869
    Bank 3 0.2299 0.5014 0.4456 0.0000 0.0000 0.0000 0.6803 0.0974 0.6459 0.1887 0.9575 0.4769 0.4504 0.9582 1.0000 0.9556 0.7275
    Bank 4 0.8583 0.8566 0.5207 0.3758 0.3719 0.4201 0.6468 0.6000 0.8354 0.6698 1.0000 0.7385 0.3892 0.9045 0.6859 0.9093 0.3070
    Bank 5 0.5428 0.7830 0.4692 0.6512 0.6574 0.8808 0.9263 1.0000 0.8971 1.0000 0.5936 1.0000 0.1517 1.0000 0.7061 1.0000 0.9960
    Bank 6 0.0000 0.6057 0.3907 0.5052 0.5278 0.4612 0.6985 0.2272 0.7982 0.1038 0.9500 0.5619 0.3991 0.8759 0.8239 0.8966 0.6888
    Bank 7 1.0000 0.7242 0.3146 0.2013 0.2044 0.5621 0.9202 0.8346 0.7806 0.7830 0.8661 0.9263 0.0354 0.8629 0.7630 0.8760 0.6752
    Bank 8 0.3396 0.8750 1.0000 0.0738 0.0630 0.9602 0.4708 0.1058 0.6712 0.3019 0.8135 0.5831 0.5301 0.9476 0.8854 0.9278 1.0000
    Bank 9 0.4652 0.7065 0.5681 0.4765 0.4928 0.6510 0.0000 0.0000 0.0000 0.7547 0.0000 0.6706 0.3367 0.7808 0.8185 0.6994 0.7615
    Bank
    0.4866 0.7268 0.6712 0.1208 0.1178 0.8025 0.8624 0.3194 0.8447 0.0000 0.6722 0.0000 0.4319 0.9495 0.8069 0.9558 0.5239
    10
    Bank
    0.2219 0.6439 0.0000 0.5638 0.5830 0.6738 0.8167 0.8136 0.5325 0.7736 0.8453 0.6964 0.2057 0.9537 0.6128 0.9326 0.7380
    11
    Bank
    0.3075 0.9974 0.7248 0.4228 0.4027 1.0000 0.5652 0.3026 0.9587 0.4717 0.8570 0.4370 0.0000 0.9294 0.7662 0.9356 0.5780
    12
    Bank
    0.7914 0.4799 0.4363 0.3356 0.3551 0.4851 0.8089 0.3749 0.5129 0.1792 0.9347 0.1959 0.4987 0.8978 0.8302 0.8909 0.7011
    13
    Bank
    0.9893 0.3138 0.0300 0.3221 0.3589 0.1442 0.9714 0.7257 0.5584 0.5377 0.3768 0.5632 0.4944 0.7139 0.8358 0.7498 0.1020
    14
    Bank
    0.9091 0.7252 0.5773 0.8591 0.8798 0.3926 1.0000 0.8471 0.3192 0.7736 0.7196 0.3998 1.0000 0.0000 0.0000 0.0000 0.8630
    15
    Bank
    0.7594 0.3800 0.5387 0.4228 0.4629 0.4947 0.8879 0.4115 0.4176 0.3868 0.5970 0.6606 0.2967 0.8692 0.8601 0.8614 0.0000
    16
    Bank
    0.6257 0.0000 0.3507 0.4161 0.4887 0.2300 0.8959 0.8314 0.4399 0.7264 0.7895 0.5976 0.0047 0.8663 0.8936 0.8848 0.6169
    17

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  16. V.K. Viswanatha Raju and VVS Kesava Rao

    CA AQ ME EQ LI
    Bank
    CA1 CA2 CA3 AQ1 AQ2 AQ3 ME1 ME2 ME3 EQ1 EQ2 EQ3 EQ4 LI1 LI2 LI3 LI4
    Bank
    0.4465 0.8623 0.4319 1.0000 1.0000 0.5887 0.7777 0.8105 1.0000 0.8208 0.8273 0.6653 0.0188 0.8911 0.5240 0.9168 0.2439
    18
    Bank
    0.6497 0.4814 0.5547 0.5638 0.6067 0.4474 0.7935 0.4115 0.6614 0.4528 0.8877 0.5550 0.4112 0.8018 0.7783 0.8259 0.6897
    19
    Bank
    0.6230 1.0000 0.7560 0.7181 0.6926 0.8568 0.9050 0.8848 0.9716 0.8208 0.6125 0.6499 0.1985 0.8721 0.8216 0.8888 0.8850
    20

    Maximum and minimum absolute differences
    The maximum (  max ) and the minimum (  min ) differences are found from the absolute
    difference of the compared series and the referential series.
     max =1.00;  min =0.00;

    Grey relation coefficient
    Grey relational coefficient  is determined from the following equation as discussed in step 9
    of section 3.6
     min  p max
    i ( j ) 
    xi ( j )  p max

    Model Calculation:
    For example for bank3 and ME1
    max = 1.00; min = 0.00; p = 0.5; xi(j) = 0.6803 (from absolute differences table)
    0  0.5 *1
    i ( j ) 
    0.6803  0.5 *1 = 0.4236
    Gray correlation coefficient (ij): Maximum and minimum absolute differences are found
    as discussed in step-4.2.2 to 4.2.3 in methodology. The grey relation coefficient is determined
    as discussed in step-4.2.4 and are presented in Table-19.

    Table 19 Grey relation coefficients for the 1st financial year
    CA AQ ME HQ LI
    Banks
    CA1 CA2 CA3 AOl A 02 A03 ME1 ME 2 ME 3 EOl E02 EOS E04 LI1 LI2 LB LI4
    Bank l 0.4359 0.4100 0.4977 0.6287 0.6274 0.3836 0.3902 0.4773 0.3699 0.5579 0.3902 0.5364 0.5461 0.3368 0.4015 0.3365 0.3378
    Bank
    0.6516 0.6268 0.7958 0.9613 0.9360 0.7006 0.4101 0.6197 0.4973 0.7571 0.4204 0.6188 0.6497 0.3643 0.3742 0.3625 0.4600
    2
    Bank
    0.6850 0.4993 0.5288 1.0000 1.0000 1.0000 0.4236 0.8370 0.4363 0.7260 0.3431 0.5118 0.5261 0.3429 0.3333 0.3435 0.4073
    3
    Bank
    0.3681 0.3686 0.4899 0.5709 0.5735 0.5434 0.4360 0.4545 0.3744 0.4274 0.3333 0.4037 0.5623 0.3560 0.4216 0.3548 0.6196
    4
    Bank
    0.4795 0.3897 0.5159 0.4343 0.4320 0.3621 0.3506 0.3333 0.3579 0.3333 0.4572 0.3333 0.7672 0.3333 0.4146 0.3333 0.3342
    5
    Bank
    1.0000 0.4522 0.5613 0.4974 0.4865 0.5202 0.4172 0.6875 0.3852 0.8281 0.3448 0.4708 0.5561 0.3634 0.3777 0.3580 0.4206
    6
    Bank
    0.3333 0.4084 0.6138 0.7129 0.7098 0.4708 0.3521 0.3747 0.3904 0.3897 0.3660 0.3506 0.9339 0.3669 0.3959 0.3634 0.4255
    7
    Bank
    0.5955 0.3636 0.3333 0.8713 0.8880 0.3424 0.5151 0.8254 0.4269 0.6235 0.3807 0.4616 0.4854 0.3454 0.3609 0.3502 0.3333
    8
    Bank
    0.5180 0.4144 0.4681 0.5120 0.5036 0.4344 1.0000 1.0000 1.0000 0.3985 1.0000 0.4271 0.5976 0.3904 0.3792 0.4169 0.3963
    9
    Bank
    0.5068 0.4076 0.4269 0.8054 0.8094 0.3839 0.3670 0.6102 0.3718 1.0000 0.4266 1.0000 0.5365 0.3449 0.3826 0.3434 0.4883
    10
    Bank
    0.6926 0.4371 1.0000 0.4700 0.4617 0.4260 0.3797 0.3806 0.4842 0.3926 0.3717 0.4179 0.7085 0.3440 0.4493 0.3490 0.4039
    11

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  17. Financial Performance Ranking of Nationalized Banks Through Integrated Ahm-Gra-Dea Method

    CA AQ ME HQ LI
    Banks
    CA1 CA2 CA3 AOl A 02 A03 ME1 ME 2 ME 3 EOl E02 EOS E04 LI1 LI2 LB LI4
    Bank
    0.6192 0.3339 0.4082 0.5418 0.5539 0.3333 0.4694 0.6230 0.3428 0.5146 0.3685 0.5336 1.0000 0.3498 0.3949 0.3483 0.4638
    12
    Bank
    0.3872 0.5103 0.5340 0.5984 0.5847 0.5076 0.3820 0.5715 0.4936 0.7361 0.3485 0.7185 0.5006 0.3577 0.3759 0.3595 0.4163
    13
    Bank
    0.3357 0.6144 0.9434 0.6082 0.5822 0.7761 0.3398 0.4079 0.4724 0.4818 0.5703 0.4703 0.5028 0.4119 0.3743 0.4001 0.8306
    14
    Bank
    0.3548 0.4081 0.4641 0.3679 0.3624 0.5602 0.3333 0.3712 0.6103 0.3926 0.4100 0.5557 0.3333 1.0000 1.0000 1.0000 0.3668
    15
    Bank
    0.3970 0.5682 0.4814 0.5418 0.5193 0.5027 0.3602 0.5485 0.5449 0.5638 0.4558 0.4308 0.6276 0.3652 0.3676 0.3673 1.0000
    16
    Bank
    0.4442 1.0000 0.5877 0.5458 0.5057 0.6850 0.3582 0.3755 0.5320 0.4077 0.3878 0.4555 0.9906 0.3660 0.3588 0.3611 0.4477
    17
    Bank
    0.5282 0.3670 0.5365 0.3333 0.3333 0.4593 0.3913 0.3815 0.3333 0.3786 0.3767 0.4291 0.9637 0.3594 0.4883 0.3529 0.6721
    18
    Bank
    0.4349 0.5095 0.4741 0.4700 0.4518 0.5278 0.3865 0.5485 0.4305 0.5248 0.3603 0.4739 0.5487 0.3841 0.3911 0.3771 0.4203
    19
    Bank
    0.4452 0.3333 0.3981 0.4105 0.4193 0.3685 0.3559 0.3611 0.3398 0.3786 0.4494 0.4348 0.7158 0.3644 0.3783 0.3600 0.3610
    20

    5.5. Financial soundness ranking of banks
    Optimistic grey relation grade of the banks are determined by solving the linear programming
    problem as discussed in step-4.3 using grey relation coefficient. Lingo code is developed for
    linear programming problem and is solved through LINGO 8.0 solver. Similarly, pessimistic
    grey relation grade of the banks are determined by solving the linear programming problem as
    discussed in step-4.3. From the optimistic and pessimistic grades of the banks, normalized grey
    relation grade is calculated and the financial soundness of the banks is ranked. Financial
    soundness of banks for the 1st financial year is shown in Table-20.

    Table 20 Financial soundness ranking of banks for the 1st financial year

    Bank Γi Γi i() Rank Bank Γi Γi i() Rank
    Bank l 0.7901 1.0966 0.3152 9 Bank 11 0.7309 1.0374 0.1220 17
    Bank 2 0.9412 1.2477 0.8083 3 Bank 12 0.8058 1.1122 0.3662 8
    Bank 3 0.9744 1.2809 0.9165 2 Bank 13 0.8202 1.1267 0.4133 7
    Bank 4 0.7690 1.0755 0.2464 13 Bank 14 0.7881 1.0946 0.3087 10
    Bank 5 0.6935 1.0000 0.0000 20 Bank 15 0.7670 1.0735 0.2398 14
    Bank 6 0.8266 1.1331 0.4344 6 Bank 16 0.7844 1.0909 0.2966 11
    Bank 7 0.7748 1.0812 0.2651 12 Bank 17 0.7573 1.0638 0.2081 16
    Bank 8 0.9273 1.2338 0.7628 4 Bank 18 0.6966 1.0030 0.0099 19
    Bank 9 1.0000 1.3065 1.0000 1 Bank 19 0.7608 1.0673 0.2196 15
    Bank 10 0.9080 1.2144 0.6997 5 Bank 20 0.6989 1.0054 0.0177 18
    In the proposed AHM-GRA-DEA integrated method, financial soundness ranking of the
    banks is made according to the normal grey relational degree. From table **, it is observed that
    Bank 9 ranks first with its degree of 1.000, followed by Bank 2 and Bank 12 with the degree of
    0.9189 and 0.9143, respectively. Last rank is obtained with Bank 20 with a grey relation degree
    in 0.0000.
    Similarly ranking of the banks through the proposed integrated method is determined for
    remaining financial years and the financial soundness of banks for 2nd financial year to 5th
    financial year is shown in the Table-21 to Table-24.

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  18. V.K. Viswanatha Raju and VVS Kesava Rao

    Table 21 Financial soundness ranking of banks for 2nd financial year
    Integrated AHM- GRA-DEA
    Bank
    Γi Γi i() Rank
    Bank l 0.8233 1.1768 0.5001 6
    Bank 2 0.8811 1.2346 0.6637 4
    Bank 3 0.9872 1.3408 0.9638 2
    Bank 4 0.7544 1.1079 0.3052 13
    Bank 5 0.7824 1.1359 0.3845 10
    Bank 6 0.7766 1.1301 0.3680 11
    Bank 7 0.6465 1.0000 0.0000 20
    Bank 8 0.8883 1.2418 0.6840 3
    Bank 9 0.8337 1.1872 0.5295 5
    Bank 10 1.0000 1.3535 1.0000 1
    Bank 11 0.7434 1.0970 0.2743 14
    Bank 12 0.7174 1.0710 0.2007 17
    Bank 13 0.8011 1.1546 0.4374 9
    Bank 14 0.7690 1.1225 0.3466 12
    Bank 15 0.8171 1.1707 0.4828 7
    Bank 16 0.7392 1.0928 0.2624 16
    Bank 17 0.8015 1.1551 0.4387 8
    Bank 18 0.7173 1.0708 0.2003 18
    Bank 19 0.7399 1.0934 0.2642 15
    Bank 20 0.7169 1.0705 0.1993 19

    Table 22 Financial soundness ranking of banks for 3rd financial year
    Integrated AHM-GRA-DEA
    Bank
    Γi Γi i() Rank
    Bank 1 0.6895 1.0236 0.0707 18
    Bank 2 0.7855 1.1196 0.3580 7
    Bank 3 0.8407 1.1748 0.5232 5
    Bank 4 0.7655 1.0997 0.2983 12
    Bank 5 0.8815 1.2156 0.6454 3
    Bank 6 0.7407 1.0748 0.2239 15
    Bank 7 0.6759 1.0100 0.0299 19
    Bank 8 0.8621 1.1962 0.5873 4
    Bank 9 1.0000 1.3341 1.0000 1
    Bank 10 0.7806 1.1147 0.3433 9
    Bank 11 0.6965 1.0306 0.0916 17
    Bank 12 0.7450 1.0791 0.2368 14
    Bank 13 0.7807 1.1148 0.3437 8
    Bank 14 0.8072 1.1414 0.4231 6
    Bank 15 0.7759 1.1101 0.3294 10
    Bank 16 0.7675 1.1017 0.3042 11
    Bank 17 0.9023 1.2364 0.7076 2
    Bank 18 0.7006 1.0347 0.1039 16
    Bank 19 0.7630 1.0972 0.2908 13
    Bank 20 0.6659 1.0000 0.0000 20

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  19. Financial Performance Ranking of Nationalized Banks Through Integrated Ahm-Gra-Dea Method

    Table 23 Financial soundness ranking of banks for 4th financial year
    Integrated AHM- GRA-DEA
    Bank
    Γi Γi i() Rank
    Bank 1 0.7651 1.0412 0.1493 19
    Bank 2 0.7860 1.0620 0.2247 15
    Bank 3 0.9749 1.2510 0.9091 2
    Bank 4 0.9256 1.2016 0.7304 4
    Bank 5 0.8400 1.1160 0.4203 11
    Bank 6 0.8525 1.1285 0.4656 9
    Bank 7 0.7239 1.0000 0.0000 20
    Bank 8 0.8638 1.1398 0.5066 7
    Bank 9 1.0000 1.2761 1.0000 1
    Bank 10 0.8548 1.1308 0.4739 8
    Bank 11 0.7676 1.0437 0.1583 18
    Bank 12 0.8387 1.1148 0.4158 12
    Bank 13 0.8297 1.1058 0.3831 14
    Bank 14 0.9230 1.1991 0.7212 5
    Bank 15 0.8400 1.1161 0.4205 10
    Bank 16 0.7815 1.0576 0.2085 16
    Bank 17 0.9282 1.2043 0.7399 3
    Bank 18 0.8835 1.1596 0.5780 6
    Bank 19 0.8338 1.1098 0.3978 13
    Bank 20 0.7712 1.0473 0.1712 17

    Table 24 Financial soundness ranking of banks for 5th financial year
    Integrated AHM-GRA-DEA
    Bank
    Γi Γi i() Rank
    Bank 1 0.7857 1.078252 0.2675 18
    Bank 2 0.8450 1.1376 0.4703 9
    Bank 3 0.9476 1.2401 0.8208 2
    Bank 4 0.8492 1.1417 0.4845 8
    Bank 5 0.7993 1.0919 0.3141 15
    Bank 6 0.8375 1.1300 0.4444 11
    Bank 7 0.7660 1.0585 0.2001 19
    Bank 8 0.8341 1.1266 0.4329 12
    Bank 9 0.9400 1.2326 0.7951 3
    Bank 10 0.8601 1.1527 0.5219 7
    Bank 11 0.7075 1.0000 0.0000 20
    Bank 12 0.8133 1.1059 0.3619 14
    Bank 13 0.7951 1.0877 0.2996 16
    Bank 14 1.0000 1.2925 1.0000 1
    Bank 15 0.9148 1.2074 0.7088 5
    Bank 16 0.8818 1.1744 0.5961 6
    Bank 17 0.9227 1.2152 0.7357 4
    Bank 18 0.7876 1.0801 0.2740 17
    Bank 19 0.8404 1.1329 0.4543 10
    Bank 20 0.8179 1.1105 0.3776 13

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  20. V.K. Viswanatha Raju and VVS Kesava Rao

    Table 25 Financial soundness ranking of banks for

    1st financial year to 5th financial year
    Financial years Average
    Bank
    1st year 2nd year 3rd year 4th year 5th year rank
    Bank 1 9 6 18 19 18 16
    Bank 2 3 4 7 15 9 7
    Bank 3 2 2 5 2 2 2
    Bank 4 13 13 12 4 8 9
    Bank 5 20 10 3 11 15 12
    Bank 6 6 11 15 9 11 10
    Bank 7 12 20 19 20 19 20
    Bank 8 4 3 4 7 12 3
    Bank 9 1 5 1 1 3 1
    Bank 10 5 1 9 8 7 4
    Bank 11 17 14 17 18 20 18
    Bank 12 8 17 14 12 14 14
    Bank 13 7 9 8 14 16 11
    Bank 14 10 12 6 5 1 6
    Bank 15 14 7 10 10 5 8
    Bank 16 11 16 11 16 6 13
    Bank 17 16 8 2 3 4 5
    Bank 18 19 18 16 6 17 17
    Bank 19 15 15 13 13 10 15
    Bank 20 18 19 20 17 13 19
    Average ranking is made by considering the average rank of the banks during 5 financial
    years. Average ranking of the banks is shown in the Table-25. From the results, it is observed
    that Bank 9 is obtained first rank on an average. Bank 9 obtained financial soundness rankings
    of 1st, 5th, 1st, 1st and 3rd respectively in the years in 1st year, 2nd year, 3rd year, 4th year and 5th
    year respectively. Bank 3 is ranked as second having ranks 2nd, 2nd, 5th, 2nd and 2nd in 1st year,
    2nd year, 3rd year, 4th year and 5th year respectively. Bank 7 is positioned in the last rank since
    the bank obtained poor average ranks of 12th, 20th, 19th, 20th and 19th rank in 1st year, 2nd year,
    3rd year, 4th year and 5th year respectively.

    6. CONCLUDING REMARKS
    Due to radical changes in the banking sector in the recent years, the banks all around the world
    have improved their supervision quality and techniques. In evaluating the function of the banks,
    many of the developed countries are now following uniform financial rating system (CAMEL
    RATING). CAMEL rating system does not consider the relative weights of the performance
    dimensions and their enablers while ranking of the banks. In this thesis, five performance
    dimensions and seventeen enablers are considered to rank the banks through integrated method
    AHM-GRA-DEA. The relative weights of the performance dimensions and their enablers are
    determined through AHM. Grey relation coefficient of the banks is determined using grey
    relation analysis. These coefficients are used in the optimistic and pessimistic additive DEA
    models to arrive the normalized compromise grade. Then the banks are ranked according to the
    descending order of the normalized compromise grade. Choosing a priori weights of attributes,
    using AHM, in the proposed models is an important matter. Equal weight assumption might not
    be acceptable for decision-makers in selecting the alternatives based on the multiple criteria.

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