Decision Making: Applications in Management and Engineering Vol. 2, Issue 2, 2019, pp. 138-158. ISSN: 2560-6018 eISSN: 2620-0104 DOI: https://doi.org/10.31181/dmame2003079b * Corresponding author. E-mail addresses: sanjibb@acm.org (S. Biswas), gautam.bandyopadhyay@dms.nitdgp.ac.in (G. Bandyopadhyay), banhi.guha@gmail.com (B. Guha), malay.bhattacharjee100@gmail.com (M. Bhattacharjee), AN ENSEMBLE APPROACH FOR PORTFOLIO SELECTION IN A MULTI-CRITERIA DECISION MAKING FRAMEWORK Sanjib Biswas 1*, Gautam Bandyopadhyay 2, Banhi Guha 3 and Malay Bhattacharjee 2* 1 Calcutta Business School, Diamond Harbour Road, Bishnupur, West Bengal, India 2 Department of Management Studies, National Institute of Technology, Durgapur, West Bengal, India 3 Amity University, Kolkata, West Bengal, India Received: 2 February 2019; Accepted: 10 August 2019; Available online: 23 August 2019. Original scientific paper Abstract: Investment in Mutual Funds (MF) has generated increasing interest among the investors over last few decades as it provides an opportunity for flexible and transparent choice of funds to diversify risk while having return potential. MF are essentially a portfolio wherein investors’ funds are invested in the securities traded in the capital market while sharing a common objective. However, selection and management of different asset classes pertaining to a particular MF are done by an active fund manager under regulatory supervision. Hence, for an individual investor, it is important to assess the performances of the MF before investment. Performances of MF depend on several criteria based on risk-return measures. Hence, selection of MF is subject to satisfying multiple criteria. In this paper, we have adopted an ensemble approach based on a two-stage framework. Our sample consists of the open ended equity large cap funds (direct plan) in India. In the first stage, the efficiencies of the funds are analyzed using DEA for primary selection of the funds. In order to rank the funds based on risk and return parameters for investment portfolio formulation, we have used MABAC approach in the second stage wherein criteria weights have been calculated using the Entropy method. Keywords: Mutual Fund, Portfolio Selection, Multi-Criteria Decision Making, Data Envelopment Analysis (DEA), Entropy, Multi-Attribute Border Approximation Area Comparisons (MABAC). mailto:sanjibb@acm.org mailto:gautam.bandyopadhyay@dms.nitdgp.ac.in mailto:banhi.guha@gmail.com mailto:malay.bhattacharjee100@gmail.com An ensemble approach for portfolio selection in a multi-criteria decision making framework 139 1. Introduction The aftermath of the economic liberalization, Indian Capital Market (ICM) has witnessed significant changes in investment pattern. With the development of Information and Communication Technology (ICT), there is no dearth of information regarding available investment opportunities. Moreover, with increasing efforts from the Govt. of India (GOI), MF have emerged as a preferred choice for common investors because of many reasons. First, it provides reportedly high return as compared to other popular investment options like Fixed Deposits (FD), National Savings Certificates (NSC), Public Provident Funds (PPF), and other postal savings. Alongside, with increasing awareness and available information, risk can also be brought down to an affordable level by carefully evaluating the performances of the MF for the prudent selection of funds to invest. The concept of MF resembles the selection of portfolio wherein the active fund managers invest the total amount invested in other asset classes such as stocks. The objective is to generate sizeable return out of the investment made in the portfolio while minimizing the risk through diversification i.e. by appropriate selection of the securities and allocating optimum weights dynamically (Gupta et al., 2018). MF in India have a long stint with ICM since the inception of Unit Trust of India (UTI) in 1963. Recent reports(AMFI, India, 2018)indicate a significant growth in the asset base of the Indian MF Industry (IMI) from INR 5.05 trillion (31st March, 2008) to INR 22.20 trillion (February, 2018)despite the event of bankruptcy of the renowned US bank Lehman Brothers in September, 2008. Therefore, a large number of investors have been attracted by the promising nature of IMI. However, in order to ensure the possibility of considerable return at an affordable risk, one has to select the funds apt to his/her risk appetite and financial goal. With this preamble, in this study, we have focused on open ended equity MF(direct plans) in India belonging to the large cap segment. The equity MF segment accounts for around 50.7% share of the total asset base of the industry in February, 2018 as reported by AMFI. Unlike the close ended funds (CF), open ended funds (OF) allow the investors to buy and sell the units of the funds on a continuous basis, which means the new investors are allowed to enter at convenience and so as the existing investors can exit whenever needed. Moreover, for CF the unit capital is fixed and also there is a limit on sales. In other words, OF allow greater flexibility for the investors than CF. Large cap funds show relatively stable movements in the return as compared to the mid-cap and small cap funds. We have considered direct plans only since, unlike regular plans, they impose less pressure on expense ratio as no intermediate commission is involved. In essence, we like to perceive the performance of MFs from a common investors’ point of view without imposing significant burden on Net Assets Value (NAV). In our approach, we have used Non-Parametric Methods (NPM). Literatures manifest comparatively less evidence of such methods than their traditional parametric counterparts (Babalos et al., 2011). Selection of MF needs to satisfy the objectives pertaining to several criteria based on risk and return and time horizon, etc. Therefore, among NPM, DEA has been a popular method, though, moderate evidences of the use of MCDM techniques have been found in the state-of-the art. The reason lies in the fundamental use of DEA to assess and differentiate between the efficient and non- efficient Decision Making Units (DMU). MCDM techniques allow to rank the DMU based on a number of criteria. Hence, for identifying efficient DMU or MF while ranking them based on performance parameters, we propose a two-stage assessment framework. The rest of the paper proceeds as follows. Section 2 highlights some of the related work while in the section 3 we discuss the research methodology. Section 4 Biwas et al/Decis. Mak. Appl. Manag. Eng. 2 (2) (2019) 138-158 140 summarizes the results and put forward necessary discussions on the same. Finally, section 5 concludes the paper and posits some future scope of research. 2. Related Work A plethora of research has been conducted on MF for understanding the nature and setting performance measurement framework with an objective to inflate the expected utility while reducing the risk level. In one of the seminal works in the stated field, Markowitz postulated the mean-variance model related to efficiently diversified portfolio (Markowitz, 1952). In the following works, the researchers (Tobin, 1958; Markowitz, 1959; Sharpe, 1966; Jensen, 1968; Treynor, 1965) further explained and extended the framework by introducing new risk measures such as semi-variance and risk adjusted performance metrics such as reward to volatility ratio, alpha and reward to variability ratio based on the Capital Assets Pricing Model (CAPM). The objective was to assess portfolio performance with respect to the benchmark with an objective to minimize the systematic risk which is represented by beta. The authors exhibited that unsystematic risk can be reduced through diversification of the portfolio. Based on these measures, several researchers and practitioners worked on evaluating the performances of the MF (Kacperczyk et al., 2005; Pedersen &Rudholm­Alfvin, 2003; Eling & Schuhmacher, 2007; Plantinga & de Groot, 2002; Redman et al., 2000). In the Indian context also, across different periods, many researchers (Barua&Verma, 1991; Jaydev, 1996; Gupta, 2000; Sehgal&Jhanwar, 2008; Tripathy, 2004; Anand & Murugaiah, 2006; Anitha et al., 2011; Arora, 2015; Kundu, 2009) worked on selection of funds based the criteria like Sharpe ratio, Jensen ratio, and Sortino ratio, alpha, beta, NAV, timing to market, and selectivity skill following traditional statistical approaches. Over the years apart from the traditional parametric approaches, applied operations research techniques have also been adopted by the researchers. The authors (Pendaraki et al., 2004; Sharma & Sharma, 2006) have applied goal programming to evaluate the performances of MF for formulating the portfolio. DEA has been a widely accepted method by the researchers and practitioners (Murthi& Choi, 2001; Murthi et al., 1997; Anderson et al., 2004; Sengupta, 2003; Daraio & Simar, 2006; Babalos et al., 2015; McMullen & Strong, 1998; Wilkens & Zhu, 2001; Tarim& Karan, 2001; Galagedera & Silvapulle, 2002; Chang, 2004; Carlos Matallín et al., 2014; Nguyen-Thi-Thanh, 2006; Chu et al., 2010; Tsolas, 2011; Morey & Morey, 1999; Basso & Funari, 2001; Briec et al., 2004; Zhao et al., 2011; Jaro & Na, 2006; Kooli et al., 2005; Haslem & Scheraga, 2003)among the non-parametric applied operations research techniques. The researchers have considered the variables like standard deviation, expense ratio, loads, turnover, beta, costs, fund size, variance, percentage of periods with negative return, lower semi-variance, sales charges, operating expenses, cash percentage, P/E ratio, P/B ratio, total assets, lower mean, lower semi-skewness, and excess kurtosis as input while considering the variables like return, deviations from median return, capital flow, skewness, Sharpe ratio, upper semi-variance, upper semi- skewness, and Jensen’s α as output in assessing the performances of the funds under study. There has been another string of the literature in which MCDM techniques are applied for selection of MF (Pendaraki et al., 2005; Lin et al., 2007; Gladish et al., 2007; Chang et al., 2010; Babalos et al., 2011; Alptekin, 2009; Karmakar et al., 2018; Pendaraki & Zopounidis, 2003; Sielska, 2010). Attribute based classification approaches like UTADIS (UTilités Additives DIScriminantes) (Pendaraki et al., 2005; Lin et al., 2007), fuzzy MCDM techniques (Gladish et al., 2007), distance based MCDM methods like TOPSIS (Lin et al., 2007; Chang et al., 2010; Alptekin, 2009; Karmakar An ensemble approach for portfolio selection in a multi-criteria decision making framework 141 et al., 2018; Sielska, 2010) and EDAS (Karmakar et al., 2018), outranking methods such as PROMETHEE (Sielska, 2010) and PROMETHEE II (Pendaraki&Zopounidis, 2003) have been selected for portfolio selection issue based on the parameters like Sharpe ratio, Sortinoratio, Treynorratio, Jensen’s α, AUM, beta, standard deviation, NAV, annualized return, average return, Information ratio, and R-squared. In this context, in paper (Babalos et al., 2011) the authors used Stochastic Multi-criteria Acceptability Analysis (SMAA-2) framework for assessing performances of MF. Predominantly, objective weight method using Euclidean Distance has been applied for calculating criteria weight. However, some authors like Chang et al. (2010) experimented with different distance measures for examining performances of the MF. 3. Data and Methodology 3.1. Development of the framework In this study, we have followed a non-parametric two stage framework wherein we have ranked the funds under study. In the first stage, we have applied DEA to appraise the efficiencies of the funds for a primary level selection. For a refined selection in a common setting for investment choice among the relatively efficient portfolios, at stage two the MCDM technique like MABAC has been used. The entropy method has been employed for calculation of criteria weight in this regard. Figure 1 depicts the framework followed in this study. We have started our analysis with total 48 number of open ended equity large cap funds under direct plan. In the seminal works of Markowitz (1952, 1959), the underline assumption considered first two central moments of the utility function of the return which is treated as a normal distribution. However, the studies (Lau et al., 1990; Cambell & Hentsche, 1992) arguably reported that portfolio returns are always not normally distributed in practice. Hence, it is imperative to consider higher moments. Average investors prefer lower value of Kurtosis (Scott & Horvath, 1980) as it entails a higher degree of sensitivity of the funds with respect to non-favorable market condition. In view of this, for filling the gap in the literature in Indian context, this study considers Kurtosis as one of the inputs. Expense ratio puts load on the profitability as it covers the management fees and operating expense. The third quartile return has a typical significance in the sense that it indicates relative closeness to the highest value than the average return. The ratio PSV to NSV signifies inclination of the deviation of the return from the mean towards the higher side which essentially acts as a favorable proposition for the investors. We have used standard Variable Returns to Scale (VRS) model as it resembles real life situation compared to Constant Returns to Scale (CRS) which reflects the proportionate change in the output with respect to the input (Ali & Seiford, 1990). Further, we have calculated super efficiency in order to discriminate the funds to a considerable extent. Biwas et al/Decis. Mak. Appl. Manag. Eng. 2 (2) (2019) 138-158 142 Figure 1. Research Framework The higher value of net assets of a fund indicates the greater possibility of a good return. The Sharpe ratio, α, and Sortino ratio specify the excess return with respect to risk, i.e. risk-adjusted performance while beta captures the systematic risk. To what extent, the portfolio return with respect to the benchmark, i.e. index, adjusts the volatility of the return is reflected in the value of Information ratio which stands beneficial for the investors. The value of R-squared manifests the nature of diversification of the portfolio, which leads to reduction of unsystematic risk. 3.2. Sample In our study, we focus on open ended and large cap equity mutual funds under direct plan. In this context, we have excluded the fixed maturity plan, and plans suspended for sales which otherwise leaves lesser chance to gain more at calculated risk. For spotting the funds, we have referred the Value research online data base and subsequently for collecting information on the performance criteria. Appendix 1 shows the descriptive statistics of the total 48 funds selected initially for the study. Returns of the last 12 quarters (i.e. Sep 2015 to Jun 2018) have been considered for calculating distribution based parameters used in DEA. 3.3. Data Envelopment Analysis (DEA) DEA evaluates a set of peer entities (homogenous) i.e. Decision Making Units (DMUs) having multiple inputs or outputs. As introduced by Charnes et al. (1978), this technique has gained extensive importance by the researchers in measuring performance efficiency in terms of the frontiers or envelop rather than the central tendency as in the case of fitting a regression model. In DEA, the efficiency of the homogenous entities is calculated by using the linear programming method. Calculations for input oriented, constant return to scale (CRS) are as follows: min 𝜃 Subject to: ∑ xij n j=1 λj ≤ θxit i = 1,2, … , m; Input Constraint (1) ∑ yrj n j=1 λj ≥ yrt r = 1,2, … , s; Output Constraint (2) Where, 𝜆𝑗 ≥ 0 ∀ 𝑖, 𝑗, 𝑟 For variable return to scale (VRS) the sets of equations are: min 𝜃 Stage 1 DEA Input/ Output Variables Input: Kurtosis; Expense Ratio Output: Third quartile return; ratio between positive semi-variance (PSV) to negative semi-variance (NSV) Stage 2 MABAC Efficiency based selection Final Ranking Portfolio Selection Criteria Net Assets, 5-Year Annualized Return, Sharpe Ratio, Sortino Ratio, Information Ratio, Alpha, R-Squared, and Beta. Entropy Method for Criteria Weight Funds under study An ensemble approach for portfolio selection in a multi-criteria decision making framework 143 Subject to: ∑ xij n j=1 λj ≤ θxit i = 1,2, … , m; Input Constraint (3) ∑ yrj n j=1 λj ≥ yrt r = 1,2, … , s; Output Constraint (4) Where, ∑ λj n j=1 = 1 ; λj ≥ 0 ∀ i, j, r If two or more DMUs are found to be efficient (i.e. θ = 1 or 100%) then the Super- efficiency value is calculated to discriminate them. For VRS the super efficiency is calculated as below: min 𝜃 Subject to ∑ xij n j=1 λj ≤ θxit i = 1,2, … , m; Input Constraint (5) ∑ yrj n j=1 λj ≥ yrt r = 1,2, … , s; Output Constraint (6) Where, ∑ λj n j=1 = 1; λj ≥ 0 ∀ i, j, r ; j ≠ t. 3.4. Entropy Method It is an objective method for calculating criteria weights based on relative information content wherein, higher value of the entropy (degree of disorder) indicates more information content for the respective criterion (Shannon, 1948). The steps are as given below where, 𝑎𝑖 : i th alternative where i = 1,2,3,…..m; 𝑐𝑗 : j th criterion where j = 1,2,3,…..n; 𝑥𝑖𝑗 : j th criterion value for the ith alternative; Step1. Normalization of the criteria. For this purpose, we have used the enhanced accuracy method of normalization Zeng et al. (2013) as mentioned in (Jahan & Edwards, 2015). Accordingly, the normalized matrix R = [𝑟𝑖𝑗 ]𝑚 ×𝑛 is given by: 𝑟𝑖𝑗 = 1- 𝑥𝑗 𝑚𝑎𝑥 −𝑥𝑖𝑗 ∑ (𝑥𝑗 𝑚𝑎𝑥−𝑥𝑖𝑗) 𝑚 𝑖=1 (Beneficial Criteria) (7) 𝑟𝑖𝑗 = 1- 𝑥𝑖𝑗−𝑥𝑗 𝑚𝑖𝑛 ∑ (𝑥𝑖𝑗−𝑥𝑗 𝑚𝑖𝑛)𝑚𝑖=1 (Non-beneficial Criteria) (8) Step 2. Entropy calculation for the criterion Entropy of the jth criterion is given by: 𝐻𝑗 = - ∑ 𝑓𝑖𝑗 ln 𝑓𝑖𝑗 𝑚 𝑖=1 ln 𝑚 , 𝑖 = 1,2, … 𝑚; 𝑗 = 1,2, . . 𝑛 (9) Where, 𝑓𝑖𝑗 = 𝑟𝑖𝑗 ∑ 𝑟𝑖𝑗 𝑚 𝑖 , 𝑖 = 1, 2, … 𝑚; 𝑗 = 1,2, … (10) Step 3. Calculation of the entropy weight for the criterion Entropy weight of the jth criterion is determined by: 𝑤𝑗 = 1−𝐻𝑗 𝑛−∑ 𝐻𝑗 𝑛 𝑗=1 , where ∑ 𝑤𝑗 𝑛 𝑗=1 = 1 (11) Biwas et al/Decis. Mak. Appl. Manag. Eng. 2 (2) (2019) 138-158 144 3.5. Multi-Attribute Border Approximation Area Comparisons (MABAC) Since its proposal (Pamučar & Ćirović, 2015), this method has drawn significant attention from the researchers for its inherent computational ease and stability. Unlike TOPSIS, this method classifies the performances of the criteria into two areas such as Upper Approximation Area (UAA) for ideal solutions and Lower Approximation Area (LAA) for non-ideal solutions instead of calculating the distance of any solution from the ideal and non-ideal solutions. In a sense, this method examines the relative strength and weakness of each alternative with respect to the others pertaining to each criterion (Roy et al., 2016). This method has been widely applied by the researchers for solving multi-criteria decision making problems such as railway management (Sharma et al., 2018; Vesković et al., 2018)medical tourism site selection (Roy et al., 2018) and selection of hotels (Yu et al., 2017). Let, D is the initial decision matrix represented by 𝑎𝑖 : i th alternative where i = 1,2,3,…..m; 𝑐𝑗 : j th criterion where j = 1,2,3,…..n; 𝑥𝑖𝑗 : j th criterion value for the ith alternative; The broad steps under this method are given below. Step 1. Normalization of the criteria values 𝑟𝑖𝑗 = (𝑥𝑖𝑗− 𝑥𝑖 −) (𝑥𝑖 +− 𝑥𝑖 − ) ; For beneficial criteria (12) 𝑟𝑖𝑗 = (𝑥𝑖𝑗− 𝑥𝑖 + ) (𝑥𝑖 −− 𝑥𝑖 + ) ; For non-beneficial criteria (13) Where, 𝑥𝑖 + and 𝑥𝑖 − are the maximum and minimum criteria values respectively. Step 2. Construction of weighted normalization matrix (Y) Elements of Y are given by: 𝑦𝑖𝑗 = 𝑤𝑗 (𝑟𝑖𝑗 + 1) ; Where, 𝑤𝑗 are the criteria weight. (14) Step 3. Determination of the Border Approximation Area (BAA) The elements of the Border Approximation Area (BAA) T is given by: 𝑡𝑗 = (∏ 𝑦𝑖𝑗 𝑚 𝑖=1 ) 1/𝑚 (15) Where, m is the total number of alternatives &𝑡𝑗 corresponds to each criterion. Step 4. Calculation of the matrix Q related to the separation of the alternatives from BAA Q = Y-T (16) A particular alternative 𝑎𝑖 is said to be belonging to the Upper Approximation Area (UAA) i.e. 𝑇+ if 𝑞𝑖𝑗 > 0 or Lower Approximation Area (LAA) i.e. 𝑇 − if 𝑞𝑖𝑗 < 0or BAA i.e. T if 𝑞𝑖𝑗 = 0. The alternative 𝑎𝑖 is considered to be the best among the others if more numbers of criteria pertaining to it possibly belong to 𝑇+. Step 5. Ranking of the alternatives It is done according to the final values of the criterion functions as given by Si = ∑ qij n j=1 for j = 1,2, … n and i = 1,2, … m (17) Higher the value, the better is the rank. In this study for carrying out DEA, we have used Lingo (version 11) software while for MCDM related calculations, Microsoft Office excel (version 2010) is utilized. An ensemble approach for portfolio selection in a multi-criteria decision making framework 145 4. Results and discussions We have considered total 48 funds initially. However, before analyzing them using DEA, we have checked whether the condition of the required number of DMUs is satisfied or not. In this regard, though there are several studies, we have followed one of the widely accepted study conducted by Banker et al. (1989). According to the study, the rule of the thumb is n >= max {p × q, 3(p + q)} where, p be the number of inputs and q is the number of outputs used in the analysis, and n is the number of DMUs to be considered. Our model has two inputs and two outputs. Hence, it satisfies the condition. The top 20 funds (i.e. DMUs) based on the result of DEA considering VRS model is given in the table 1 while the details is included in the appendix 2. The performance criteria values of the above funds (Table 1) are given in the appendix 1. We then have used MCDM model for ranking the above mentioned funds. For calculating criteria weights, we have used a modified Entropy method. The results are listed in tables 2-3. After calculating the criteria weights, we then proceed to the stage 2 i.e. ranking of the funds (primary selection through DEA) using the MABAC technique. The results are given in tables 4-6. From the result, it is evident that the top five funds (i.e. A27, A19, A38, A22 and A25; the names are given in appendix 1) are rated 4-star and 5-star by Value research and except one of them, and their risk grades are above average or more. On the other hand, bottom five funds (i.e. A40, A42, A21, A3 and A5; the names are given in appendix 1) are rated 2-star or below and having an overall average risk grade. Hence, this study also conforms to the market based rating of the funds by Value research. In order to check the dependability of the result obtained from MABAC, we have also ranked the funds selected from DEA result using TOPSIS technique. In line with the method suggested by Hwang and Yoon (1981), we have obtained the rankings as given in the table 7. For checking consistency with MABAC based ranking, we have performed Spearman’s Rank Correlation test using IBM SPSS 22, which is 0.952 (significant at 0.01 level). Hence, the result obtained from MABAC is acceptable. Biwas et al/Decis. Mak. Appl. Manag. Eng. 2 (2) (2019) 138-158 146 T a b le 1 . D E A r e su lt ( T o p 2 0 F u n d s) F u n d s u n d e r st u d y K u rt o si s K u rt o si s (N o rm a li z e d )( In p u t) E x p e n se R a ti o (I n p u t) P S V / N S V (O u tp u t) Q 3 ( O u tp u t) V R S R e su lt R a n k V R S D M U 3 -0 .9 9 4 2 1 8 2 9 7 0 .2 2 8 3 5 7 7 8 5 0 .5 1 0 .6 9 2 5 2 4 2 0 6 6 .3 2 5 0 .2 7 7 2 0 D M U 5 0 .4 3 0 0 5 2 7 9 6 1 1 .0 5 1 .1 9 0 7 5 9 4 5 3 7 .5 1 2 5 0 .4 1 9 6 1 7 D M U 1 0 0 .0 6 8 7 4 5 8 7 5 0 .8 0 4 2 5 0 9 7 8 2 .0 9 1 .7 1 2 9 8 8 5 7 3 6 .0 6 5 1 7 D M U 1 3 -1 .3 9 2 0 7 2 4 5 1 0 .0 1 2 8 0 8 1 8 8 0 .1 5 1 .0 2 4 9 4 6 6 6 7 7 .3 4 7 5 1 .5 2 7 2 2 D M U 1 4 -1 .0 6 9 7 3 6 0 7 3 0 .1 8 7 4 4 3 7 3 2 0 .1 5 0 .6 9 7 8 2 1 4 7 9 6 .6 5 7 5 0 .8 3 4 2 1 1 D M U 1 5 -0 .9 8 6 2 8 6 2 2 9 0 .2 3 2 6 5 5 2 2 5 1 .2 6 1 .6 5 8 3 9 9 1 9 8 .5 3 7 5 1 7 D M U 1 9 -0 .8 6 7 6 8 1 9 8 1 0 .2 9 6 9 1 2 6 8 6 0 .4 4 1 .1 6 7 1 8 5 8 9 2 9 .8 0 2 5 1 .4 6 3 D M U 2 1 -1 .0 4 7 2 4 5 0 8 9 0 .1 9 9 6 2 8 9 0 7 0 .4 3 0 .7 0 8 5 7 5 8 5 1 6 .5 2 2 5 0 .3 2 7 6 1 8 D M U 2 2 -0 .9 1 4 6 4 0 3 5 9 0 .2 7 1 4 7 1 5 5 5 0 .5 6 1 .1 7 7 3 4 2 7 8 9 9 .7 4 2 5 1 .0 2 6 D M U 2 4 -1 .0 2 0 2 0 4 2 8 6 0 .2 1 4 2 7 9 0 8 5 0 .1 7 0 .7 0 2 1 0 1 3 0 9 6 .5 9 2 5 0 .7 3 4 9 1 3 D M U 2 5 -0 .7 5 6 9 4 1 7 1 1 0 .3 5 6 9 0 9 5 9 8 0 .7 5 0 .7 0 3 9 5 1 6 5 9 8 .0 9 0 .3 1 6 9 1 9 D M U 2 7 -1 .3 4 0 7 0 3 7 1 5 0 .0 4 0 6 3 8 7 6 4 2 .9 4 0 .7 0 3 0 1 8 8 2 5 1 2 .0 2 2 5 1 7 D M U 3 2 -1 .4 1 5 7 1 3 3 7 1 0 1 .1 5 1 .0 3 8 4 4 5 7 3 5 7 .1 8 1 7 D M U 3 6 -0 .9 6 8 7 9 4 4 0 .2 4 2 1 3 1 9 5 5 0 .2 9 0 .7 0 6 5 9 5 0 6 6 6 .6 1 0 .4 5 8 6 1 6 D M U 3 7 -1 .4 1 4 5 6 6 8 3 5 0 .0 0 0 6 2 1 1 7 1 0 .2 9 1 .0 2 7 5 7 9 3 9 7 .0 4 5 3 .0 3 4 3 1 D M U 3 8 -0 .9 5 0 0 8 2 1 3 3 0 .2 5 2 2 6 9 8 9 5 1 .3 2 1 .5 2 8 3 5 8 0 1 3 7 .0 7 0 .7 8 1 9 1 2 D M U 4 0 -1 .0 4 6 7 9 3 8 1 7 0 .1 9 9 8 7 3 3 9 7 0 .2 9 0 .7 0 3 3 5 6 9 4 5 6 .6 0 7 5 0 .4 6 8 9 1 5 D M U 4 2 -1 .0 6 3 8 9 2 4 5 6 0 .1 9 0 6 0 9 6 8 9 0 .2 1 0 .7 0 2 1 4 8 7 6 8 6 .6 8 5 0 .6 2 6 4 1 4 D M U 4 3 -1 .4 0 3 7 3 3 1 3 2 0 .0 0 6 4 9 0 6 5 9 0 .2 2 1 .0 3 3 5 2 9 5 3 2 7 .2 4 1 .4 1 0 3 4 D M U 4 8 -1 .0 7 2 4 5 1 5 0 9 0 .1 8 5 9 7 2 5 6 2 0 .1 2 0 .6 9 1 0 7 3 6 2 9 6 .5 8 7 5 1 .2 5 5 An ensemble approach for portfolio selection in a multi-criteria decision making framework 147 Table 2. Normalization Table Alt. C1 C2 C3 C4 C5 C6 C7 C8 A3 0.9450 0.9338 0.9315 0.9315 0.8427 0.9350 1.0000 0.9600 A5 0.9477 0.9561 0.8910 0.8883 0.9688 0.9165 0.8951 0.9850 A10 0.9450 0.9446 0.9688 0.9694 0.9866 0.9611 0.9161 1.0000 A13 0.9453 0.9381 0.9564 0.9514 0.9839 0.9499 0.9930 0.9600 A14 0.9460 0.9406 0.9470 0.9477 0.9304 0.9453 1.0000 0.9600 A15 1.0000 0.9627 0.9315 0.9333 0.9831 0.9350 0.9510 0.8650 A19 0.9454 0.9834 0.9844 1.0000 0.9914 0.9815 0.7832 0.9800 A21 0.9453 0.9359 0.9377 0.9369 0.8585 0.9389 1.0000 0.9550 A22 0.9446 0.9809 0.9782 0.9928 0.9902 0.9784 0.7762 0.9850 A24 0.9449 0.9400 0.9470 0.9459 0.9346 0.9446 1.0000 0.9550 A25 0.9459 0.9509 0.9751 0.9712 0.9917 0.9655 0.9231 0.9550 A27 0.9446 1.0000 1.0000 0.9946 1.0000 1.0000 0.8531 0.7850 A32 0.9445 0.9314 0.9315 0.9279 0.9634 0.9363 0.9930 0.9600 A36 0.9449 0.9383 0.9377 0.9405 0.9144 0.9399 1.0000 0.9550 A37 0.9445 0.9333 0.9470 0.9441 0.9756 0.9452 0.9930 0.9700 A38 0.9841 0.9808 0.9502 0.9423 0.9848 0.9491 0.9301 0.9400 A40 0.9456 0.9371 0.9439 0.9459 0.8882 0.9435 1.0000 0.9550 A42 0.9445 0.9375 0.9439 0.9441 0.8936 0.9426 1.0000 0.9550 A43 0.9445 0.9345 0.9470 0.9441 0.9774 0.9457 0.9930 0.9600 A48 0.9478 0.9401 0.9502 0.9477 0.9405 0.9459 1.0000 0.9600 Table 3. Hj values and criteria weights Hj 0.748 0.748 0.748 0.748 0.747 0.748 0.747 0.747 wj 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 Table 4. Normalization Result Alt. C1 C2 C3 C4 C5 C6 C7 C8 A3 0.009 0.035 0.371 0.387 0.000 0.221 1.000 0.814 A5 0.058 0.359 0.000 0.000 0.802 0.000 0.531 0.930 A10 0.009 0.193 0.714 0.726 0.915 0.534 0.625 1.000 A13 0.016 0.098 0.600 0.565 0.898 0.399 0.969 0.814 A14 0.028 0.134 0.514 0.532 0.558 0.345 1.000 0.814 A15 1.000 0.456 0.371 0.403 0.892 0.221 0.781 0.372 A19 0.017 0.759 0.857 1.000 0.945 0.779 0.031 0.907 A21 0.014 0.065 0.429 0.435 0.100 0.268 1.000 0.791 A22 0.003 0.722 0.800 0.935 0.938 0.741 0.000 0.930 A24 0.007 0.125 0.514 0.516 0.584 0.336 1.000 0.791 A25 0.026 0.284 0.771 0.742 0.947 0.587 0.656 0.791 A27 0.002 1.000 1.000 0.952 1.000 1.000 0.344 0.000 A32 0.001 0.000 0.371 0.355 0.767 0.237 0.969 0.814 A36 0.008 0.100 0.429 0.468 0.456 0.280 1.000 0.791 A37 0.000 0.028 0.514 0.500 0.845 0.344 0.969 0.860 A38 0.714 0.720 0.543 0.484 0.904 0.390 0.688 0.721 Biwas et al/Decis. Mak. Appl. Manag. Eng. 2 (2) (2019) 138-158 148 Alt. C1 C2 C3 C4 C5 C6 C7 C8 A40 0.021 0.083 0.486 0.516 0.289 0.324 1.000 0.791 A42 0.000 0.088 0.486 0.500 0.323 0.313 1.000 0.791 A43 0.000 0.045 0.514 0.500 0.856 0.350 0.969 0.814 A48 0.061 0.126 0.543 0.532 0.622 0.351 1.000 0.814 Table 5. Border Approximation Area Matrix BAA 0.1347 0.1552 0.1907 0.1919 0.2066 0.1730 0.2181 0.2189 Table 6. Ranking of the Funds Fund A3 A5 A10 A13 A14 A15 A19 A21 A22 A24 Sum (Si) -0.134 -0.154 0.101 0.056 0.002 0.073 0.173 -0.101 0.144 -0.005 Rank 19 20 6 8 12 7 2 18 4 13 Fund A25 A27 A32 A36 A37 A38 A40 A42 A43 A48 Sum (Si) 0.111 0.173 -0.050 -0.048 0.019 0.156 -0.050 -0.051 0.017 0.017 Rank 5 1 15 14 9 3 16 17 11 10 Table 7. TOPSIS Ranking Fund A3 A5 A10 A13 A14 A15 A19 A21 A22 A24 TOPSIS Rank 20 15 7 8 12 3 4 19 5 13 Fund A25 A27 A32 A36 A37 A38 A40 A42 A43 A48 TOPSIS Rank 6 1 14 16 10 2 17 18 9 11 5. Conclusion We have made an attempt to assess the funds from two perspectives such as efficiency and performance. Accordingly, we have filtrated the funds through a two stage process using DEA at stage 1 and MABAC at stage 2. The rationale behind this study lies in the selection of the funds to form an investment portfolio based on their return distribution and performance parameters encompassing risk-return tradeoff. In effect, this study not only has adjudged the funds on efficiency dimension, but also sets out to establish a ranking based on risk-return criteria. Our results conform to the market based rating of the funds. A combination of DEA-Entropy-MABAC turns this study considerably different from the existing contributions in the Indian context as far as the approach is concerned. The results of this study provide the investors a broader perspective for selection of the portfolio. However, future research shall be required to focus more clinical approach by considering fundamental parameters and stock level analysis. It is important to analyze the stocks on which the fund managers invest the amount invested by the investors both on fundamental dimension and organizational dimensions to ascertain the decision and establish a causal relationship among the stock performance and MF performance. Further, the efficiencies of the fund houses need to be examined. There are requirements to investigate the relationship between investors’ sentiments and market performance of the MF. Also, a consistency between the performances of the funds belonging to different categories can be thought of. Finally, the framework used in this study can be further explored for different other applications. An ensemble approach for portfolio selection in a multi-criteria decision making framework 149 Acknowledgement: The authors would like to express sincere gratitude to all reviewers for providing valuable comments for further improvement. The first draft of this paper has been presented during the First International Conference on “Frontiers of Operations Research & Business Studies (FORBS 2018)” organized by Calcutta Business School in collaboration with Operational Research Society of India (ORSI), Kolkata Chapter (Oct 11-13, 2018) and subsequently some modifications have been incorporated in response to the reviewers’ comments. References Ali, A. I., & Seiford, L. M. (1990).Translation invariance in data envelopment analysis. Operations research letters, 9(6), 403-405. Alptekin, N. (2009). Performance evaluation of Turkish type a mutual funds and pension stock funds by using TOPSIS method. International Journal of Economics and Finance Studies, 1(2), 11-22. Anand, S., & Murugaiah, V. (2006). Analysis of components of investment performance: An empirical study of mutual funds in India. 10th Indian Institute of Capital Markets Conference, IU, Hyderabad, India. Anderson, R., Brockman, C., Giannikos, C., & McLeod, R. (2004). A non-parametric examination of real estate mutual fund efficiency. International Journal of Business and Economics, 3, 225–238. Anitha, R., Devasenathipathi, T., & Radhapriya, C. (2011). Comparative analysis of market returns and fund flows with reference to mutual funds. International Journal of Research in Commerce, IT & Management, 1(4), 45­58. Arora, K. (2015). Risk­adjusted performance evaluation of Indian mutual fund schemes.Paradigm, 19(1), 79­94. Babalos, V., Mamatzakis, E. C., & Matousek, R. (2015). The performance of US equity mutual funds. Journal of Banking & Finance, 52, 217-229. Babalos, V., Philippas, N., Doumpos, M., & Zopounidis, C. (2011). Mutual Funds Performance Appraisal Using a Multi Criteria Decision Making Approach. Financial Engineering Laboratory (University of Crete). Babalos, V., Philippas, N., Doumpos, M., & Zopounidis, C. (2011). Mutual funds performance appraisal using a Multi-Criteria Decision Making approach. Financial Engineering Laboratory (University of Crete). Banker, R. D., Charnes, A., Cooper, W. W., & Clarke, R. (1989).Constrained game formulations and interpretations for data envelopment analysis. European Journal of Operational Research, 40(3), 299-308. Basso, A., &Funari, S. (2001). Data Envelopment Analysis Approach to Measure the Mutual Fund Performance. Europen Journal of Operational Research, 135, 477-492. Barua, K. S., & Verma, J. R. (1991). Master shares: A bonanza for large investors. Vikalpa, 16(1), 29­34. Biwas et al/Decis. Mak. Appl. Manag. Eng. 2 (2) (2019) 138-158 150 Briec, W., Kerstens, K., & Lesourd, J.B (2004). Single-period Markowitz portfolio selection, performance gauging, and duality: a variation on the Luenberger shortage function. Journal of Optimization Theory and Applications, 120(1), 1–27. Cambell, J.Y., & Hentschel, L. (1992). No news is good news: An asymmetric model of changing volatility of stock returns. Journal of Financial Economics, 31, 281-318. Carlos Matallín, J., Soler, A., &Tortosa-Ausina, E. (2014). On the informativeness of persistence for evaluating mutual fund performance using partial frontiers. Omega, 42(1), 47–64. DOI: 10.1016/j.omega.2013.03.001. Chang, C.H., Lin, J.J., Lin, J.H., & Chiang, M.C. (2010). Domestic open­end equity mutual fund performance evaluation using extended TOPSIS method with different distance approaches. Expert Systems with Applications, 37(6), 4642­4649. Chang, K.P. (2004). Evaluating mutual fund performance: an application of minimum convex input requirement set approach. Computers & Operations Research, 31(6), 929–940. Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429-444. Chu, J., Chen, F., & Leung, P. (2010). ETF performance measurement – data envelopment analysis. Service Systems and Service Management (ICSSSM), 7th International Conference on, IEEE, 28–30 June, 2010, Tokyo, Japan, 1–6. Daraio, C., & Simar, L. (2006). A robust nonparametric approach to evaluate and explain the performance of mutual funds. European Journal of Operational Research, 175, 516–542. Eling, M., & Schuhmacher.F. (2007). Does the choice of performance measure influence the evaluation of hedge funds? Journal of Banking and Finance, 31(9), 2632­ 2647. Galagedera, D., & Silvapulle, P. (2002). Australian Mutual Fund Performance Appraisal Using Data Envelopment Analysis. Managerial Finance, 28(9) 60–73. Gladish, B.P., Jones, D.F. Tamiz, M., & Bilbao Terol, A. (2007). An interactive three stage model for mutual funds portfolio selection. Omega, 35, 75–88. Gupta, S., Bandyopadhyay, G., Biswas, S., &Upadhyay, A. (2018). A hybrid machine learning and dynamic nonlinear framework for determination of optimum portfolio structure. Paper presented at the 6th International Conference on Innovations in Computer Science & Engineering (ICICSE), Hyderabad, India, June 2018. Gupta, A. (2000). Investment performance of Indian mutual funds: An empirical study. Finance India, 14(3), 833­866. Haslem, J., & Scheraga, C. (2003). Data envelopment analysis of Morningstar’s large- cap mutual funds. Journal of Investing, 12 (4), 41–48. Hwang, C.L., & Yoon, K. (1981) Multiple attribute decision making: Methods and applications. Heidelberg: Springer. Jahan, A., Edwards, K. L. (2015). A state-of-the-art survey on the influence of normalization techniques in ranking: Improving the materials selection process in engineering design. Materials & Design, 65, 335-342. An ensemble approach for portfolio selection in a multi-criteria decision making framework 151 Joro, T., & Na, P. (2006). Portfolio performance evaluation in a mean–variance– skewness framework. European Journal of Operational Research, 175 (1), 446–461. Jayadev, M. (1996). Mutual fund performance: An analysis of monthly returns. Finance India, 10 (1), 73­84. Jensen, M. (1968). The performance of mutual funds in the period 1945–64.Journal of Finance, 23, 389– 416. Kacperczyk, M., Sialm, C. & Zheng, L. (2005).On the industry concentration of actively managed equity mutual funds.The Journal of Finance, 60(4), 1983­2011. Karmakar, P., Dutta, P., & Biswas, S. (2018). Assessment of mutual fund performance using distance based multi-criteria decision making techniques-An Indian perspective. Research Bulletin, 44(1), 17-38. Kooli, M., Morin, F., & Sedzro, K. (2005).Evaluation des mesures de performance des hedge funds’, Communication at International Conference of the French Association of Finance, June, Paris, France. Kundu, A. (2009). Stock selection performance of mutual fund managers in India: an empirical study. Journal of Business and Economic Issues, 1(1), 69­73. Lau, A.H. L., Lau, H.S., & Wingender, J.R. (1990). The distribution of stock returns: New evidence against the stable model. Journal of Business and Economic Statistics, 8, 217- 223. Lin, J. J., Chang, C. H., & Chiang, M. C. (2007). A comparison of usual indices and extended TOPSIS Methods in mutual funds’ performance evaluation. Journal of Statistics & Management Systems 10(6), 869­883. Markowitz, H. M. (1959). Portfolio selection: Efficient diversification of investment. John Wiley & Sons, New York. Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91. McMullen, P.R., & Strong, R.A. (1998). Selection of mutual funds using data envelopment analysis. Journal of Business and Economic Studies, 4(1), 1–12. Morey, M.R., & Morey, R.C. (1999). Mutual fund performance appraisals: a multi- horizon perspective with endogenous benchmarking. Omega 27(2), 241–258. Murthi, B. P. S., & Choi, Y. K. (2001). Relative performance evaluation of mutual funds: A non-parametric approach. Journal of Business Finance and Accounting, 28, 853–876. Murthi, B. P. S., Choi, Y. K., & Desai, P. (1997). Efficiency of mutual funds and portfolio performance measurement: A non-parametric approach. European Journal of Operational Research, 98(2), 408–418. Nguyen-Thi-Thanh, H. (2006). On the Use of Data Envelopment Analysis in Hedge Fund Selection, Working Paper, Universitéd’ Orléans. http://repec.org/mmf2006/up.18346.1145733238.pdf (Accessed on 10th July, 2018). Pamučar, D., & Ćirović, G. (2015). The selection of transport and handling resources in logistics centers using Multi-Attributive Border Approximation area Comparison (MABAC). Expert Systems with Applications, 42(6), 3016-3028. Biwas et al/Decis. Mak. Appl. Manag. Eng. 2 (2) (2019) 138-158 152 Pedersen, C. S., & Rudholm­Alfvin, T. (2003). Selecting risk­adjusted shareholder performance measure. Journal of Asset Management, 4(3), 152­172. Pendaraki, K., Doumpos, M., & Zopounidis, C. (2004). Towards a goal programming methodology for constructing equity mutual fund portfolios. Journal of Asset Management, 4(6), 415–428. Pendaraki, K., Zopounidis, C., & Doumpos, M. (2005). On the construction of mutual fund portfolios: A multicriteria methodology and an application to the Greek market of equity mutual funds. European Journal of Operational Research, 163(2), 462­481. Pendaraki, K., & Zopounidis, C. (2003). Evaluation of equity mutual funds’ performance using a multicriteria methodology. Operational Research, 3(1), 69-90. Plantinga, A., & de Groot. D. (2002). Risk­adjusted performance measures and implied risk attitudes. Journal of Performance Measurement, 6, 9­22. Redman, A. L., Gullett, N. S., & Manakyan, H. (2000). The performance of global and international mutual funds”, Journal of Financial and Strategic Decisions, 13(1), 75­85. Roy, J., Ranjan, A., Debnath, A., & Kar, S. (2016). An extended MABAC for multi-attribute decision making using trapezoidal interval type-2 fuzzy numbers.arXiv preprint arXiv:1607.01254. Roy, J., Chatterjee, K., Bandyopadhyay, A., & Kar, S. (2018). Evaluation and selection of medical tourism sites: A rough analytic hierarchy process based multi­attributive border approximation area comparison approach. Expert Systems, 35(1), e12232. Scott, R.C., & Horvath, P.A. (1980).On the direction of preference for moments of higher order than the variance. Journal of Finance, 35, 915-919. Sehgal, S., &Jhanwar, N. (2008). On stock selection skills and market timing abilities of mutual fund managers in India. International Research Journal of Finance and Economics, 15, 307­317. Sengupta, J. (2003). Efficiency tests for mutual fund portfolios. Applied Financial Economics, 13, 869–876. Sielska, A. (2010). Multicriteria rankings of open-end investment funds and their stability.Operations research and decisions, 1(20), 112-129. Sharma, H. K., Roy, J., Kar, S., & Prentkovskis, O. (2018). Multi Criteria Evaluation Framework for Prioritizing Indian Railway Stations Using Modified Rough AHP- MABAC Method. Transport and Telecommunication Journal, 19(2), 113-127. Sharma, H.P., & Sharma, D.K. (2006). A multi­objectivedecision­making approach for mutual fund portfolio. International Business & Economics Research Journal, 4, 13– 24. Sharpe, W.F. (1966). Mutual fund performance.Journal of Business, 39, 119­138. Shannon, C.E. (1948). The mathematical theory of communication.Bell System Technical Journal, 27, 379­423. Tarim, S.A., & Karan, M.B. (2001). Investment fund performance measurement using weightrestricted data envelopment analysis: an application to the turkish capital market. Russian and East European Finance and Trade, 37(5), 64–84. An ensemble approach for portfolio selection in a multi-criteria decision making framework 153 Tobin, J. (1958). Liquidity preference as behavior towards risk.Review of Economic Studies, 25(1), 65­86. Treynor, J. (1965). How to rate management of investment funds. Harvard Business Review 43, 63–75. Tripathy, N. P. (2004). An empirical analysis on performance evaluation of mutual funds in India: A study on equity linked saving schemes. The IUP Journal of Applied Finance, 10 (7), 307­317. Tsolas, I. (2011). Natural resources exchange traded funds: performance appraisal using DEA modeling’, The Business and Economics Research Journal, 4(2), 250–259. Vesković, S., Stević, Ž.,Stojić, G., Vasiljević, M., &Milinković, S. (2018). Evaluation of the railway management model by using a new integrated model DELPHI-SWARA- MABAC. Decision Making: Applications in Management and Engineering, 1(2), 34-50. Wilkens, K., & Zhu, J. (2001). Portfolio evaluation and benchmark selection: a mathematical programming approach. The Journal of Alternative Investments, 4 (1), 9–19. Yu, S. M., Wang, J., & Wang, J. Q. (2017). An interval type-2 fuzzy likelihood-based MABAC approach and its application in selecting hotels on a tourism website. International Journal of Fuzzy Systems, 19(1), 47-61. Zeng, Q.L., Li, D.D., & Yang, Y.B. (2013). VIKOR method with enhanced accuracy for multiple criteria decision making in healthcare management. Journal of Medical System, 37, 1–9. Zhao, X., Wang, S., & Lai, K.K. (2011). Mutual funds performance evaluation based on endogenous benchmarks. Expert Systems with Applications, 38 (4), 3663–3670. © 2018 by the authors. Submitted for possible open access publication under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Biwas et al/Decis. Mak. Appl. Manag. Eng. 2 (2) (2019) 138-158 154 A p p e n d ix 1 . D e sc ri p ti v e S ta ti st ic s S / L F u n d R a t in g R is k G ra d e N e t A ss e ts (C r) (C 1 ) 5 -Y e a r a n n u a li ze d R e t (C 2 ) S h a r p e R a ti o (C 3 ) S o rt i n o R a ti o (C 4 ) In fo rm a t io n R a ti o (C 5 ) A lp h a (C 6 ) R - S q u a r e d (C 7 ) B e ta (C 8 ) S D E x p e n s e R a ti o A 1 A d it y a B ir la S u n L if e F o cu se d E q u it y F u n d - D ir e ct P la n * * * * B e lo w A v e ra g e 4 2 3 9 .3 9 2 1 .9 8 0 .3 6 0 .5 5 -0 .1 6 - 0 .1 2 0 .9 3 0 .9 2 1 3 .2 2 1 .2 6 A 2 A d it y a B ir la S u n L if e F ro n tl in e E q u it y F u n d - D ir e ct P la n * * * * B e lo w A v e ra g e 2 1 3 8 0 . 4 2 2 1 .3 9 0 .3 8 0 .6 0 -0 .3 8 0 .1 3 0 .9 4 0 .9 3 1 3 .3 2 1 .3 1 A 3 A d it y a B ir la S u n L if e I n d e x F u n d - D ir e ct P la n * A b o v e A v e ra g e 1 4 2 .9 1 1 6 .1 9 0 .3 1 0 .5 0 -4 .7 5 - 1 .0 9 1 .0 0 0 .9 9 1 3 .8 4 0 .5 1 A 4 A x is B lu e ch ip F u n d - D ir e ct P la n * * * * * L o w 2 5 6 8 .1 0 2 0 .7 7 0 .5 9 0 .7 8 0 .2 4 3 .0 6 0 .8 7 0 .8 7 1 3 .0 0 0 .9 4 A 5 B N P P a ri b a s L a rg e C a p F u n d - D ir e ct P la n * * A v e ra g e 8 9 2 .5 2 1 9 .7 1 0 .1 8 0 .2 6 -0 .5 1 - 2 .5 2 0 .8 5 0 .9 4 1 4 .2 2 1 .0 5 A 6 C a n a ra R o b e co B lu e ch ip E q u it y F u n d - D ir e ct P la n * * * B e lo w A v e ra g e 1 3 1 .6 6 1 8 .7 2 0 .4 0 0 .6 1 0 .0 9 0 .4 9 0 .9 2 0 .9 7 1 4 .0 7 1 .4 8 A 7 D H F L P ra m e ri ca L a rg e C a p F u n d - D ir e ct P la n * * * B e lo w A v e ra g e 4 1 4 .4 9 1 9 .8 5 0 .3 5 0 .6 0 -0 .3 4 - 0 .4 4 0 .9 7 0 .9 3 1 3 .1 8 1 .5 1 A 8 D S P T o p 1 0 0 E q u it y F u n d - D ir e ct P la n * H ig h 3 0 0 7 .8 0 1 7 .4 0 0 .2 5 0 .4 1 -0 .3 3 - 1 .6 9 0 .9 0 1 .0 2 1 4 .9 9 1 .4 7 A 9 E d e lw e is s L a rg e C a p F u n d - D ir e ct P la n * * * A v e ra g e 1 4 0 .8 1 2 0 .3 3 0 .3 8 0 .5 9 0 .0 0 0 .0 2 0 .9 4 1 .0 0 1 4 .2 8 0 .5 8 A 1 0 E ss e l L a rg e C a p E q u it y F u n d - D ir e ct P la n * * * B e lo w A v e ra g e 1 5 0 .6 6 1 7 .9 0 0 .4 3 0 .7 1 0 .0 9 0 .9 3 0 .8 8 0 .9 1 1 3 .4 7 2 .0 9 A 1 1 F ra n k li n I n d ia B lu e ch ip F u n d - D ir e ct P la n * * A v e ra g e 8 1 0 7 .9 4 1 8 .8 4 0 .2 3 0 .4 3 -0 .7 9 - 1 .8 7 0 .9 5 0 .9 0 1 2 .8 4 1 .1 6 A 1 2 F ra n k li n I n d ia I n d e x F u n d - N S E N if ty P la n - D ir e ct P la n * * A v e ra g e 2 5 3 .2 1 1 6 .6 4 0 .3 2 0 .5 2 -3 .6 8 - 0 .8 6 1 .0 0 0 .9 9 1 3 .7 7 0 .6 4 An ensemble approach for portfolio selection in a multi-criteria decision making framework 155 A 1 3 H D F C I n d e x F u n d - S e n se x P la n - D ir e ct P la n * * * B e lo w A v e ra g e 2 4 4 .0 4 1 6 .8 7 0 .3 9 0 .6 1 0 .0 0 0 .0 6 0 .9 9 0 .9 9 1 3 .8 4 0 .1 5 A 1 4 H D F C I n d e x F u n d N if ty 5 0 P la n - D ir e ct P la n * * * A v e ra g e 4 3 5 .8 9 1 7 .2 6 0 .3 6 0 .5 9 -1 .8 0 -0 .2 9 1 .0 0 0 .9 9 1 3 .8 4 0 .1 5 A 1 5 H D F C T o p 1 0 0 F u n d - D ir e ct P la n * * * H ig h 1 5 2 6 0 .7 9 2 0 .7 6 0 .3 1 0 .5 1 -0 .0 3 -1 .0 9 0 .9 3 1 .1 8 1 6 .9 9 1 .2 6 A 1 6 H S B C L a rg e C a p E q u it y F u n d - D ir e ct P la n * * * A v e ra g e 7 2 9 .8 2 1 8 .9 0 0 .4 1 0 .6 6 0 .2 1 0 .4 9 0 .9 5 1 .0 4 1 4 .8 5 1 .5 1 A 1 7 IC IC I P ru d e n ti a l B lu e ch ip F u n d - D ir e ct P la n * * * * L o w 1 8 7 4 7 .2 8 2 0 .6 2 0 .4 7 0 .7 3 0 .2 5 1 .2 1 0 .9 4 0 .9 3 1 3 .2 7 1 .1 7 A 1 8 IC IC I P ru d e n ti a l N if ty I n d e x F u n d - D ir e ct P la n * * A v e ra g e 3 5 7 .3 4 1 7 .2 0 0 .3 4 0 .5 6 -3 .5 5 -0 .6 2 1 .0 0 0 .9 9 1 3 .8 4 0 .5 7 A 1 9 IC IC I P ru d e n ti a l N if ty N e x t 5 0 I n d e x F u n d - D ir e ct P la n * * * * * A b o v e A v e ra g e 2 6 5 .3 6 2 4 .0 4 0 .4 8 0 .8 8 0 .2 5 2 .5 1 0 .6 9 0 .9 5 1 5 .8 5 0 .4 4 A 2 0 ID B I In d ia T o p 1 0 0 E q u it y F u n d - D ir e ct P la n * * A v e ra g e 4 1 7 .4 9 1 8 .9 4 0 .1 6 0 .2 8 -0 .7 1 -2 .6 7 0 .8 9 0 .8 9 1 3 .1 3 1 .0 6 A 2 1 ID B I N if ty I n d e x F u n d - D ir e ct P la n * * A b o v e A v e ra g e 2 2 4 .6 4 1 6 .5 2 0 .3 3 0 .5 3 -4 .2 2 -0 .7 9 1 .0 0 1 .0 0 1 3 .8 7 0 .4 3 A 2 2 ID B I N if ty J u n io r In d e x F u n d - D ir e ct P la n * * * * * A b o v e A v e ra g e 5 5 .9 9 2 3 .6 4 0 .4 6 0 .8 4 0 .2 1 2 .2 7 0 .6 8 0 .9 4 1 5 .7 9 0 .5 6 A 2 3 ID F C L a rg e C a p F u n d - D ir e ct P la n * * * B e lo w A v e ra g e 3 7 3 .2 5 1 7 .3 0 0 .4 4 0 .6 5 0 .1 7 0 .9 2 0 .9 5 0 .9 3 1 3 .2 6 1 .8 3 A 2 4 ID F C N if ty F u n d - D ir e ct P la n * * * A v e ra g e 1 1 7 .7 0 1 7 .1 7 0 .3 6 0 .5 8 -1 .6 6 -0 .3 5 1 .0 0 1 .0 0 1 3 .8 5 0 .1 7 A 2 5 In d ia b u ll s B lu e ch ip F u n d - D ir e ct P la n * * * * A v e ra g e 4 0 1 .7 5 1 8 .8 9 0 .4 5 0 .7 2 0 .2 6 1 .2 7 0 .8 9 1 .0 0 1 4 .7 0 0 .7 5 A 2 6 In v e sc o I n d ia L a rg e ca p F u n d - D ir e ct P la n * * * * L o w 1 5 2 .2 6 2 1 .0 5 0 .4 7 0 .7 2 0 .2 8 1 .2 5 0 .9 6 0 .9 2 1 2 .9 9 0 .9 6 A 2 7 JM C o re 1 1 F u n d - D ir e ct P la n * * * * * H ig h 3 6 .2 2 2 6 .6 6 0 .5 3 0 .8 5 0 .5 4 3 .9 4 0 .7 9 1 .3 4 2 0 .8 9 2 .9 4 A 2 8 JM L a rg e C a p F u n d - D ir e ct P la n * B e lo w A v e ra g e 2 8 1 8 .0 1 1 7 .2 5 0 .0 6 0 .0 9 -1 .3 1 -3 .5 7 0 .9 6 0 .8 0 1 1 .3 6 1 .6 1 A 2 9 K o ta k B lu e ch ip F u n d - D ir e ct P la n * * * B e lo w A v e ra g e 1 4 2 3 .6 0 2 0 .4 2 0 .3 5 0 .5 6 -0 .2 3 -0 .4 1 0 .9 6 0 .9 5 1 3 .5 2 1 .1 5 Biwas et al/Decis. Mak. Appl. Manag. Eng. 2 (2) (2019) 138-158 156 A 3 0 L & T I n d ia L a rg e C a p F u n d - D ir e ct P la n * * A v e ra g e 4 2 3 .8 5 1 8 .7 4 0 .2 1 0 .3 8 -0 .6 2 -2 .1 6 0 .9 2 0 .9 5 1 3 . 7 7 2 .0 4 A 3 1 L IC M F I n d e x -N if ty P la n - D ir e ct P la n * A b o v e A v e ra g e 2 3 .7 7 1 6 .3 9 0 .3 0 0 .4 9 -3 .4 9 -1 .1 7 1 .0 0 1 .0 0 1 3 . 9 6 0 .6 9 A 3 2 L IC M F I n d e x -S e n se x P la n - D ir e ct P la n * A v e ra g e 2 0 .6 9 1 5 .8 1 0 .3 1 0 .4 8 -0 .6 9 -0 .9 9 0 .9 9 0 .9 9 1 3 . 8 6 1 .1 5 A 3 3 L IC M F L a rg e C a p F u n d - D ir e ct P la n * * B e lo w A v e ra g e 2 4 5 .0 9 1 8 .0 9 0 .1 9 0 .3 2 -0 .7 7 -2 .3 5 0 .9 3 0 .9 0 1 3 . 0 2 1 .5 2 A 3 4 M o ti la l O sw a l F o cu se d 2 5 F u n d - D ir e ct P la n * * * * L o w 1 1 7 0 . 5 3 2 1 .9 4 0 .3 8 0 .5 5 -0 .0 6 0 .7 2 0 .7 2 0 .7 8 1 2 . 8 3 1 .1 5 A 3 5 P ri n ci p a l N if ty 1 0 0 E q u a l W e ig h t F u n d - D ir e ct P la n * A b o v e A v e ra g e 1 8 .1 7 1 5 .8 4 0 .2 3 0 .3 9 -1 .2 6 -2 .1 6 0 .9 8 0 .9 9 1 3 . 9 2 0 .5 0 A 3 6 R e li a n ce I n d e x F u n d - N if ty P la n - D ir e ct P la n * * A b o v e A v e ra g e 1 3 2 .9 9 1 6 .9 0 0 .3 3 0 .5 5 -2 .3 4 -0 .7 1 1 .0 0 1 .0 0 1 3 . 9 7 0 .2 9 A 3 7 R e li a n ce I n d e x F u n d - S e n se x P la n - D ir e ct P la n * * A v e ra g e 7 .6 3 1 6 .1 1 0 .3 6 0 .5 7 -0 .2 8 -0 .3 0 0 .9 9 0 .9 7 1 3 . 5 5 0 .2 9 A 3 8 R e li a n ce L a rg e C a p F u n d - D ir e ct P la n * * * * A b o v e A v e ra g e 1 0 8 9 7 .8 2 2 3 .6 2 0 .3 7 0 .5 6 0 .0 3 0 .0 0 0 .9 0 1 .0 3 1 5 . 0 6 1 .3 2 A 3 9 S B I B lu e ch ip F u n d - D ir e ct P la n * * * * * L o w 2 0 2 8 3 .9 2 2 2 .6 1 0 .4 1 0 .6 2 -0 .0 3 0 .5 3 0 .9 0 0 .8 7 1 2 . 8 3 1 .1 8 A 4 0 S B I N if ty I n d e x F u n d - D ir e ct P la n * * A v e ra g e 3 2 0 .9 9 1 6 .7 1 0 .3 5 0 .5 8 -3 .2 2 -0 .4 3 1 .0 0 1 .0 0 1 3 . 9 3 0 .2 9 A 4 1 S u n d a ra m S e le ct F o cu s F u n d - D ir e ct P la n * * * * B e lo w A v e ra g e 8 3 5 .7 0 1 8 .6 2 0 .4 3 0 .6 6 0 .0 5 0 .6 9 0 .9 5 0 .9 0 1 2 . 8 2 0 .5 5 A 4 2 T a ta I n d e x N if ty F u n d - D ir e ct P la n * * A v e ra g e 1 2 .0 6 1 6 .7 7 0 .3 5 0 .5 7 -3 .0 4 -0 .5 0 1 .0 0 1 .0 0 1 3 . 8 7 0 .2 1 A 4 3 T a ta I n d e x S e n se x F u n d - D ir e ct P la n * * * A v e ra g e 5 .8 7 1 6 .3 0 0 .3 6 0 .5 7 -0 .2 2 -0 .2 6 0 .9 9 0 .9 9 1 3 . 8 1 0 .2 2 A 4 4 T a ta L a rg e C a p F u n d - D ir e ct P la n * * * B e lo w A v e ra g e 8 0 3 .2 9 1 8 .5 0 0 .2 9 0 .4 7 -0 .4 5 -1 .1 5 0 .9 5 0 .9 5 1 3 . 5 3 0 .7 4 A 4 5 T a u ru s L a rg e ca p E q u it y F u n d - D ir e ct P la n * H ig h 3 9 .3 8 1 7 .0 4 0 .0 0 0 .0 0 -1 .2 7 -5 .3 5 0 .9 1 0 .9 9 1 4 . 4 1 2 .1 5 A 4 6 T a u ru s N if ty I n d e x F u n d - D ir e ct P la n * * * A v e ra g e 1 9 .0 6 1 7 .1 1 0 .3 7 0 .6 0 -0 .2 6 -0 .2 0 0 .9 9 0 .9 8 1 3 . 6 3 1 .2 2 A 4 7 U T I M a st e rs h a re F u n d - D ir e ct P la n * * * B e lo w A v e ra g e 5 5 3 0 . 6 6 1 9 .5 7 0 .3 0 0 .5 3 -0 .4 9 -0 .9 7 0 .9 6 0 .9 1 1 2 . 9 6 1 .4 3 A 4 8 U T I N if ty I n d e x F u n d - D ir e ct P la n * * * A v e ra g e 9 3 5 .9 4 1 7 .1 8 0 .3 7 0 .5 9 -1 .4 6 -0 .2 5 1 .0 0 0 .9 9 1 3 . 7 9 0 .1 2 An ensemble approach for portfolio selection in a multi-criteria decision making framework 157 Appendix 2. Calculation of efficiency using DEA Funds under study Input Output VRS result Rank VRS Kurtosis Kurtosis (normalized) Expense Ratio PSV/ NSV Q3 DMU1 -0.4904 0.5013 1.2600 1.0549 6.6575 16.07% 31 DMU2 -0.7490 0.3612 1.3100 1.0393 7.1600 13.37% 36 DMU3 -0.9942 0.2284 0.5100 0.6925 6.3250 27.70% 20 DMU4 -0.5445 0.4720 0.9400 0.5358 7.4000 16.62% 30 DMU5 0.4301 1.0000 1.0500 1.1908 7.5125 41.96% 17 DMU6 0.2381 0.8960 1.4800 0.7074 5.9725 9.31% 43 DMU7 -0.0014 0.7662 1.5100 0.7634 5.5975 9.27% 44 DMU8 -0.9583 0.2478 1.4700 0.6868 6.0125 10.06% 41 DMU9 -0.5300 0.4798 0.5800 0.6661 6.8850 22.95% 25 DMU10 0.0687 0.8043 2.0900 1.7130 6.0650 100% 7 DMU11 -0.5220 0.4842 1.1600 0.7371 4.7950 12.24% 38 DMU12 -1.0308 0.2085 0.6400 0.7048 6.3925 22.51% 26 DMU13 -1.3921 0.0128 0.1500 1.0249 7.3475 152.72% 2 DMU14 -1.0697 0.1874 0.1500 0.6978 6.6575 83.42% 11 DMU15 -0.9863 0.2327 1.2600 1.6584 8.5375 100% 7 DMU16 -0.5595 0.4639 1.5100 0.7604 6.7950 9.57% 42 DMU17 -1.2878 0.0693 1.1700 0.9866 6.7800 15.06% 32 DMU18 -1.0226 0.2130 0.5700 0.7052 6.5200 25.08% 22 DMU19 -0.8677 0.2969 0.4400 1.1672 9.8025 146.00% 3 DMU20 -0.0496 0.7401 1.0600 1.0686 6.1950 21.37% 27 DMU21 -1.0472 0.1996 0.4300 0.7086 6.5225 32.76% 18 DMU22 -0.9146 0.2715 0.5600 1.1773 9.7425 102.00% 6 DMU23 -1.0924 0.1751 1.8300 0.5602 6.7950 8.18% 46 DMU24 -1.0202 0.2143 0.1700 0.7021 6.5925 73.49% 13 DMU25 -0.7569 0.3569 0.7500 0.7040 8.0900 31.69% 19 DMU26 -0.7229 0.3754 0.9600 0.6534 6.3100 14.85% 33 DMU27 -1.3407 0.0406 2.9400 0.7030 12.0225 100% 7 DMU28 -0.6121 0.4354 1.6100 0.7645 3.8550 9.03% 45 DMU29 -0.5916 0.4465 1.1500 1.0974 5.9675 24.09% 24 DMU30 -0.3986 0.5510 2.0400 0.7255 6.5800 7.13% 47 DMU31 -1.0855 0.1789 0.6900 0.6874 6.5025 21.11% 28 DMU32 -1.4157 0.0000 1.1500 1.0384 7.1800 100% 7 DMU33 -1.3228 0.0504 1.5200 0.5927 5.8700 14.05% 35 DMU34 -0.8733 0.2939 1.1500 0.6444 7.5100 14.71% 34 DMU35 -0.7201 0.3768 0.5000 0.7821 4.9900 26.93% 21 DMU36 -0.9688 0.2421 0.2900 0.7066 6.6100 45.86% 16 DMU37 -1.4146 0.0006 0.2900 1.0276 7.0450 303.43% 1 DMU38 -0.9501 0.2523 1.3200 1.5284 7.0700 78.19% 12 DMU39 -0.6039 0.4398 1.1800 0.8370 7.2125 12.26% 37 DMU40 -1.0468 0.1999 0.2900 0.7034 6.6075 46.89% 15 DMU41 -0.1160 0.7042 0.5500 0.8305 5.9050 24.10% 23 DMU42 -1.0639 0.1906 0.2100 0.7021 6.6850 62.64% 14 Biwas et al/Decis. Mak. Appl. Manag. Eng. 2 (2) (2019) 138-158 158 Funds under study Input Output VRS result Rank VRS Kurtosis Kurtosis (normalized) Expense Ratio PSV/ NSV Q3 DMU43 -1.4037 0.0065 0.2200 1.0335 7.2400 141.03% 4 DMU44 -0.8221 0.3216 0.7400 0.6315 6.6900 19.13% 29 DMU45 -1.0498 0.1983 2.1500 0.4023 6.5025 6.97% 48 DMU46 -0.6233 0.4293 1.2200 0.7896 6.4950 11.76% 39 DMU47 -0.8883 0.2857 1.4300 0.7594 5.8050 10.29% 40 DMU48 -1.0725 0.1860 0.1200 0.6911 6.5875 125.00% 5