**PERFORMANCE OF UNIT TRUST FUNDS BETWEEN CONVENTIONAL AND ISLAMIC FUNDS IN MALAYSIA USING DATA ENVELOPMENT ANALYSIS** Received Date: \*date Accepted Date: \*date Published Date: \*date **HIGHLIGHTS** - The consistency of Islamic and Conventional unit trust funds in position at top rank. - The current performance of conventional and Islamic funds in Malaysia. - The best unit trust fund should be invested by investor. ABSTRACT *This study aims to analyze the current performance of unit trust funds between conventional and Islamic funds using data envelopment analysis because most Malaysians are incapable to distinguish between conventional and Islamic unit trust funds performances since they tend to assume both funds perform similarly. This paper uses 20 authorised funds by the Securities Commission Malaysia (SC) for three years by using trailing data that consists of volatility element as input and total return as output. Indeed, the funds selected do not mix asset classes of funds, instead relying solely on equity funds to create a fair and reasonable ranking. The study employs Data Envelopment Analysis by testing two different models, namely Charnes, Cooper, and Rhodes input oriented (CCR-I) model and Banker, Charnes, and Cooper input oriented (BCC-I) model. The use of two models in this study is to ensure that the results of the ranking analysis are more accurate and precise. Both models employ the input-oriented model function as a means of maximising efficiency in order to increase the number of fairies. The efficiency of Islamic funds is more consistent than that of conventional funds for both models, as several Islamic funds maintain their position at the top of the efficient rank. However, there is a significant increase in conventional funds because 80% of the selected conventional funds that are not efficient in the CCR-I model achieve the efficiency level in the BCC-I model. As a result, there are four unit trust funds that are consistent in occupying efficiency level when tested for both CCR-I model and BCC-I model whereby three out of four are Islamic funds while the other is conventional fund. The Islamic funds consist of Apex Dana Aslah, BIMB i Growth Fund, and Maybank Malaysia Growth-I Fund while KAF Tactical Fund is conventional fund. Ultimately, it is concluded that Islamic funds perform better than conventional funds in Malaysia for the 3 years period ending 31 March 2021.* ***Keywords:*** *Unit Trust Fund, Data Envelopment Analysis (DEA), Islamic Fund, Conventional Fund, Ranking, Efficiency* **INTRODUCTION** Many Malaysians are interested in increase earnings by doing personal financial planning through investments to ensure a better future. There are various types of investments made by Malaysians including investing in unit trusts or mutual funds. However, most Malaysians are unable to differentiate the performance of unit trust funds between conventional and Islamic funds because they think both funds have the same performance. People also view all unit trusts funds as being the same because they assume that conventional and Islamic unit trusts funds have the same purpose while both actually have a different purpose. Through past studies conducted by Bashir & Nawang (2011), conventional unit trust funds have higher returns and high performance than Islamic unit trust funds which have lower returns and low performance. They used risk as input and returns as output. They found that the average return was 4.57 percent and standard deviation also known as risk was 215.58 percent for Islamic unit trust funds. Meanwhile, the average return for conventional unit trust funds is 13.34 percent and the standard deviation is 7.36 percent. However, the study conducted by Hassan and his team in 2020 shows a different result where they found that the Islamic unit trust fund has better performance and return than conventional unit trust fund by using risk as input and return as output. The study shows that the mean return of the Islamic unit trust funds is 0.5 percent while the conventional unit trust funds is 0.4 percent. In measuring risk, the study shows that the risk of Islamic unit trust funds is 4.4 percent while conventional unit trust funds are 6.1 percent. Since it has different results on performance and return of both unit trust funds, therefore it is very important to carry out the study on analyzing the performance of unit trust funds between conventional and Islamic funds with a thorough analysis. **PREVIOUS STUDIES** Whether conventional or Islamic, one of the best ways to see the future of unit trust funds is by looking at the performances. Therefore, some studies had been carried out by previous researchers evaluating the efficiency of the unit trust. Efficiency information about unit trust help to motivate an investor to make an investment in unit trust and help fund manager to make better pricing and improve profitability (Saad et al., 2010). This study aims to measure the efficiency of selective conventional and Islamic unit trust firms in Malaysia during the period 2002 to 2005. As computed by the Malmquist Index, the study applies Data Envelopment Analysis (DEA) to observe efficiency, which is broken down into two components which are efficiency enhancement and technological change indexes. This paper also uses the Portfolio Turnover Ratio (PTR) and Management Expenses Ratio (MER) as Input while Return as Output. The study demonstrates that technical efficiency is a significant contributor to improve the effectiveness of the Malaysian unit trust segment. In fact, the bigger the unit trust firms' scale, the more inefficient the output is. The study shows that in evaluating the effectiveness of unit trust firms, many of the Islamic unit trust companies score higher than their conventional counterparts. The paper shows that in evaluating the effectiveness of unit trust firms, some of the Islamic unit trust companies outperform their conventional competitors. At the end of the research, the author found that the Islamic unit trusts performed better than their conventional ones during the under-review phase. The next study on DEA is the non-parametric calculation of foreign and Islamic mutual funds' results (Rubio et al., 2012). The goal of this paper is to research whether Islamic investors are losing portfolio performance due to the restricted asset universe. The input and output of this research are standard deviation and return, respectively. The overall summary on efficiency score shows that the Islamic unit trust scores 53.25 percent while the conventional unit trust fund scores 41.99 percent. Lastly, the findings are consistent with prior conclusions. In other words, there is clear proof that Islamic funds are highly effective and outperform their foreign counterparts. The results of the various DEA projections, the characterization of the asset universe, and the involvement of the financial crisis-era in the study are also robust. Majid & Maulana (2012) have researched a Comparison Study of Islamic and Conventional Unit Trust Production efficiency in Indonesia by adopting Data Envelopment Analysis and Generalized Least Square method. The authors examine the data of unit trust funds in Indonesia at the range of 2004 until 2007. The focus of the study is to determine the efficiency by using 3 inputs and 1 output. The 3 inputs are entry fee, exit fee, and expense ratio while the output is total return. The study shows that on average, there was a decline in Total Factor Productivity (TFP) production for Indonesian unit trusts. Finally, the study finds that on average, the Islamic unit trust companies performed poorly compared to their conventional counterparts. Taufiq et al., (2019) discuss the efficiency of Islamic and conventional mutual funds in Pakistan for the period of 8 years from January 2010 to December 2017. 30 Islamic unit trust funds and 30 conventional unit trust funds were employed in this research as a sample study. The study determines the effectiveness of Islamic and conventional unit trusts, along with the data envelopment analysis methodology, based on different ratios, such as the Sharpe ratio, Treynor ratio, and Jensen Alphen. The results of the data envelopment appraisal have shown that is contrast to conventional unit trusts, Islamic unit trusts are more efficient. The overall efficiency at the final part of the study which compares the weighted sum of input over output found that Islamic unit trust funds score the higher than conventional unit trust funds, which is 0.017514 and 0.004432, respectively. Finally, for the period from 2010 to 2017, the financial productivity of Islamic unit trusts in the Pakistani unit trust market was found to be better than that of conventional mutual funds. Recently, studies have been performed by Hassan et al. (2020) to develop investment literature and to provide up-to-date proof of Islamic unit trusts results using data from a sample of a global unit trust to support quantitative data. This research assesses the competitive effectiveness of Islamic and conventional unit trusts using the capital asset pricing model, the three-factor model of Fama & French, and the four-factor model of Carhart. The input and output used in this study are risks and average return respectively. Moreover, the study assessed the cost-effectiveness effect by using the data envelopment analysis tool. Researchers found some evidence that, when the size of the funds is controlled, Islamic investment underperforms conventional unit trust in four out of six models. The size of bad results ranges from model to model in the Carhart four-factor model, 32 basis points to two basis points in the Fama and French three-factor models. The study revealed that alpha(s) are only marginal when the multicollinearity factor is included in the correlation of conventional mutual funds. While comparing the load on Islamic mutual funds, the findings show that Islamic mutual funds are less volatile than conventional unit trusts when monitored for skewness where Islamic unit trust funds show that 0.5 percent and 4.4 percent for average return and risk, respectively. Meanwhile, the average return and risk are 0.4 percent and 6.1 percent respectively, for conventional unit trust funds. **METHODOLOGY** The monthly data selected is from the Morningstar Malaysia official website for each unit trust fund for 3 years based on risk and total return data starting 31 March 2018 until 31 March 2021. The data only include 20 unit trust funds, 10 of which are conventional unit trust funds and 10 of which are Islamic unit trust funds as depicted in Table 1. Moreover, F1, F2, etc in the column DMU represent the 20 unit trust funds included in this study. In addition, this study also only employs one asset class namely equity fund. **Table 1**: The list of 20 unit trust funds with asset class and management company | No. | Unit Trust Funds | DMU | Asset Class | Management Company | | --- | ---------------------------------- | --- | -------------- | --------------------------------- | | 1 | Apex Dana Aslah | F1 | Equity Islamic | Apex Investment Services Berhad | | 2 | Affin Hwang Aiiman Growth Fund | F2 | Equity Islamic | Affin Hwang Asset Management Bhd | | 3 | BIMB i Growth Fund | F3 | Equity Islamic | BIMB Investment Management Berhad | | 4 | AmIslamic Growth | F4 | Equity Islamic | AmFunds Management Berhad | | 5 | KAF Dana Adib | F5 | Equity Islamic | KAF Investment Funds Berhad | | 6 | Kenanga Ekuiti Islam Fund | F6 | Equity Islamic | Kenanga Investors Berhad | | 7 | Maybank Malaysia Growth-I Fund | F7 | Equity Islamic | Maybank Asset Management Sdn Bhd | | 8 | Phillip Dana Aman | F8 | Equity Islamic | Phillip Mutual Berhad | | 9 | PMB Shariah Index Fund | F9 | Equity Islamic | PMB Investment Berhad | | 10 | PMB Shariah Tactical Fund | F10 | Equity Islamic | PMB Investment Berhad | | 11 | Affin Hwang Equity Fund | F11 | Equity | Affin Hwang Asset Management Bhd | | 12 | AmMalaysia Equity | F12 | Equity | AmFunds Management Berhad | | 13 | Apex Malaysia Growth Trust | F13 | Equity | Apex Investment Services Berhad | | 14 | Eastspring Investments Growth Fund | F14 | Equity | Eastspring Investments Berhad | | 15 | KAF Tactical Fund | F15 | Equity | KAF Investment Funds Berhad | | 16 | Kenanga Growth Fund | F16 | Equity | Kenanga Investors Berhad | | 17 | Maybank Malaysia Growth Fund | F17 | Equity | Maybank Asset Management Sdn Bhd | | 18 | Phillip Dividend Fund | F18 | Equity | Phillip Mutual Berhad | | 19 | RHB KLCI Tracker Fund | F19 | Equity | RHB Asset Management Sdn Bhd | | 20 | AmDividend Income | F20 | Equity | AmFunds Management Berhad | **Input & Output** This study uses trailing volatility (risk) as the input. The definitions for all volatility components, such as **Alpha, Beta, R-square, Sharpe Ratio,** and **Standard Deviation**, are taken from the Morningstar Malaysia official website. On the other hand, for output, this paper used trailing total return based on trailing data related to trailing risk as of 31 March 2021 for the period of 3 years. This data can be referred in the Appendix. Moreover, the trailing return represents a fund’s annualized return over a specific time span beginning on a specific date and ending on the last day of the most recent day, month, quarter, or year. **Alpha** - Alpha calculates the correlation between a fund’s projected returns and its actual returns based on its beta. A positive alpha indicates that the fund performed better than its beta would have predicted. A negative alpha indicates that a fund has underperformed when the beta of the asset is taken into account. **Beta** - This test measures a fund’s resiliency to market fluctuations. A beta greater than one suggests that the investment is riskier than the market. If the beta is less than one, the investment is less risky than the market. **R-squared** – It represents the proportion of a fund’s fluctuations that are clarified by movements in its benchmark index. A higher R-squared value indicates a more useful beta figure. A lower R-squared is less important to the fund's success (below 70%). **Sharpe Ratio** – It displays the bonus per unit of risk as a function of standard deviation and surplus return. The higher the Sharpe ratio value, the better the risk-adjusted performance history of a fund. **Standard Deviation** – The scale of output of a portfolio is put to the test. The greater the standard deviation, the greater the portfolio’s volatility. **CCR-I Model** The input and output for unit trust funds were tested using the CCR input-oriented DEA model (CCR-I), which has a constant return to scale. The input-oriented model is more concerned with maximizing the efficiency of the decision making units (DMUs). The efficiency scores of each DMU could be calculated using the weighted sum formula. The nonlinear weighted sum formula is used to maximize the efficiency value of the evaluated DMUs and to calculate technical efficiency. The weighted sum is used to calculate the aggregate of input and output by dividing the maximum ratio of total weighted outputs by the total of weighted inputs, subject to the condition that similar ratios for each DMU be less than or equal to one. Equations (1) through (2) depict the mathematical model of weighted sum, whereas (3) through (5) depict the equality constraint for both inputs and outputs. \[h_{k} = \ \frac{u_{1}y_{10}\ + \text{\ u}_{2}y_{20}\ + \ \ldots\text{\ u}_{m}y_{m0}}{v_{1}x_{10}\ + \ v_{2}x_{20}\ + \ \ldots\ v_{s}x_{s0}} = \ \frac{\sum_{j = 1}^{m}{u_{j}y_{j0}}}{\sum_{i = 1}^{s}{v_{i}x_{i0}}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)\] \[\ \max{h_{k} = \ \frac{\sum_{j = 1}^{m}{u_{j}y_{j0}}}{\sum_{i = 1}^{s}{v_{i}x_{i0}}}}\text{\ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)\] Subject to: \[\frac{\sum_{j = 1}^{m}{u_{j}y_{\text{jk}}}}{\sum_{i = 1}^{s}{v_{i}x_{\text{ik}}}}\ \leq 1,\ k = 1,2\ldots,\ n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (3)\] \[u_{j}\ \geq 0;\left( j = 1,2,\ldots,m \right);\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (4)\] \(v_{i}\ \geq 0;\left( i = 1,2,\ldots,s \right).\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (5)\) Furthermore, the weight inputs and outputs are positive, resulting in a positive value of technical efficiency, as shown in inequalities constraints (4) and (5). The nonlinear model (3) would be converted into an equivalent linear programming model. The CCR-I multiplier model is depicted in equation (6) until (8). \[{\text{max\ }h_{0} =}{\sum_{j = 1}^{m}{u_{j}y_{j0}}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (6)\] Subject to: \[\sum_{j = 1}^{m}{u_{j}y_{\text{jk}}} - \ \sum_{i = 1}^{s}{v_{i}x_{\text{ik}}}\ \leq 0;\left( k = 1,2,\ldots,n \right);\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (7)\] \[\sum_{i = 1}^{s}{v_{i}x_{i0}} = 1;\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (8)\] \[u_{j}\ \geq 0;\left( j = 1,2,\ldots,m \right);\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (9)\] \[v_{i}\ \geq 0;\left( i = 1,2,\ldots,s \right).\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (10)\] where, \(\ y_{\text{jk}} = Output\ r\ for\ DMU\ k\) \(u_{j} = Weight\ of\ output\ j\) \(x_{\text{ik}} = Input\ i\ for\ DMU\ j\) \(v_{i} = Weight\ of\ input\ i\) \(h_{j} = Efficiency\ of\ DMU\ j\) **BCC-I Model** To make the study more reasonable, the BCC input-oriented of the DEA model (BCC-I) is used to analyse the input and output data of a unit trust fund. It is worth noting that the CCR input-minimising and output-maximising formulations produce similar results, which is not the case with the BCC model. As a result, the formulation in the input-oriented BCC model minimises the outputs given the inputs and vice versa. Furthermore, the BCC model includes an extra constant variable, \(w_{0}\), to allow for variable return to scale. The weighted sum formula for the BCC model is described in (11) until (13). \[h_{k} = \ \frac{u_{1}y_{10}\ + \text{\ u}_{2}y_{20}\ + \ \ldots\text{\ u}_{m}y_{m0}}{v_{1}x_{10}\ + \ v_{2}x_{20}\ + \ \ldots\ v_{s}x_{s0}}\ - \ w_{0} = \ \frac{\sum_{j = 1}^{m}{u_{j}y_{j0}}}{\sum_{i = 1}^{s}{v_{i}x_{i0}}} - \ w_{0}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (11)\] \[\max{h_{k} = \ \frac{\sum_{j = 1}^{m}{u_{j}y_{j0}}}{\sum_{i = 1}^{s}{v_{i}x_{i0}}}} - \ w_{0}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (12)\] Subject to: \[\frac{\sum_{j = 1}^{m}{u_{j}y_{\text{jk}}}}{\sum_{i = 1}^{s}{v_{i}x_{\text{ik}}}} - \ w_{0}\ \leq 1,\ k = 1,2\ldots,\ n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left( 13 \right)\] \[u_{j}\ \geq 0;\left( j = 1,2,\ldots,m \right);\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (14)\] \[v_{i}\ \geq 0;\left( i = 1,2,\ldots,s \right).\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (15)\] Furthermore, the inputs and outputs for weight are positive, resulting in a positive value of relative efficiency, as shown in inequalities constraints (14) and (15). The nonlinear model (13) would be transformed into an equivalent linear programming model. The multiplier model of BCC-I is depicted in equation (16) until (18). \[\max{\sum_{j = 1}^{m}{u_{j}y_{j0}}} - \ w_{0}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\left( 16 \right)\] Subject to: \[\sum_{j = 1}^{m}{u_{j}y_{\text{jk}}} - \ \sum_{i = 1}^{s}{v_{i}x_{\text{ik}}} - \ w_{0}\ \leq 0;\left( k = 1,2,\ldots,n \right);\ \ \ \ \ \ \ \text{\ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (17)\] \[\sum_{i = 1}^{s}{v_{i}x_{i0}} = 1;\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (18)\] \[u_{j}\ \geq 0;\left( j = 1,2,\ldots,m \right);\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (19)\] \[v_{i}\ \geq 0;\left( i = 1,2,\ldots,s \right).\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (20)\] where, \(y_{\text{jk}} = Output\ r\ for\ DMU\ k\) \(u_{j} = Weight\ of\ output\ j\) \(x_{\text{ik}} = Input\ i\ for\ DMU\ j\) \(v_{i} = Weight\ of\ input\ i\) \(h_{j} = Efficiency\ of\ DMU\ j\) **COMPUTATION EXPERIMENT** The purpose of this computation experiment section is to demonstrate the evaluation and analysis of the performance of the unit trust funds between conventional and Islamic by using the Data Envelopment Analysis (DEA) model, which is CCR-I and BCC-I. This study focuses on two variables of input and output, namely volatility and total return. Volatility is also known as risk, and it is made up of five components: Alpha, Beta, R-square, Sharpe Ratio, and Standard Deviation. In this study, only one type of asset class is used: equity. This is necessary to ensure that the analysis of unit trust performance is more accurate and equitable. The data of conventional and Islamic unit trust would be computed by sophisticated software, DEA Solver Learning Version 8.0 developed by Saitech Company. Figure 1 depicts screenshot of Microsoft Excel, which is installed with DEA Solver Learning Version 8.0. ![Graphical user interface, application, table, Excel Description automatically generated](6118a98417a44_media/media/image1.png) **Figure 1**: DEA-Solver software starts up interface **OVERALL PERFORMANCE OF UNIT TRUST FUNDS CCR-I AND BCC-I** In this study, decision making units (DMUs) represent the 20 unit trust funds, and each DMU has 5 inputs and 1 output in order to measure the efficiency of unit trust funds over a 3-year period using the CCR-I and BCC-I models. Figures 2 and 3 depict the overall performance of unit trust funds for both the CCR-I and BCC-I models. According to both figures, the BCC-I model has a higher accuracy in calculating the efficiency of each unit trust fund than the CCR-I model. This is clearly demonstrated by the fact that 13 unit trust funds are efficient under the BCC-I model, while only 4 unit trust funds are efficient under the CCR-I model. BCC-I model also shows that the remaining 7 unit trust funds are approaching efficiency, whereas CCR-I model shows that 13 unit trust funds are approaching efficiency and the remaining 3 unit trust funds are truly inefficient. This is because the BCC-I model has been improved from the CCR-I model in order to ensure that the analysis performed on a study is more accurate by adding an additional constant variable to the original formula which is CCR-I (Ji et al., 2015). Therefore, many inefficient unit trust funds on the CCR-I model are productive on the BCC-I model. Only Apex Dana Aslah maintained its position among all efficient unit trust funds on the CCR-I and BCC-I models. This demonstrates that Apex Dana Aslah is the best unit trust fund among the 20 in this study based on risk data and total return over 3 years as of 31 March 2021. Both figures depict the performance of unit trust funds, with the graphical view from efficiency score providing a clearer view of each fund’s level. It should be noted, however, that only unit trust funds with a score of 100% or 1 are considered efficient. Figure 2 shows the overall performance of the unit trust fund for the CCR-I model. According to the bar graph in Figure 2, there are 6 unit trust funds that score between 0.9 and 1.0, but only 4 of them are efficient: Apex Dana Aslah, BIMB I Growth Fund, Maybank Malaysia Growth-I Fund, and KAF Tactical Fund. The Maybank Malaysia Growth Fund is the only fund with a scale of 0.6 to 0.7. Furthermore, Eastpring Investments Growth Fund and Affin Hwang Equity Fund have scale efficiency ranging from 0.7 to 0.8. There are numerous unit trust funds with ratings ranging from 0.8 to 0.9 on the graph, which begins with AmDividend Income and ends with AmIslamic Growth. However, all unit trust funds from 0.8 to 0.9 are inefficient. Finally, the score efficiency bar for RHB KLCI Tracker Fund, Philip Dividend Fund, and Philip Dana Aman do not appear in the graph, indicating that these funds are the worst performing funds. ![](6118a98417a44_media/media/image2.png) **Figure 2**: Graph overall performance for unit trust funds CCR-I model The graph performance scale efficiency for the BCC-I model is depicted in Figure 3. It also shows a significant increase in efficiency score from its previous model, the CCR-I model. The graph clearly shows that 13 unit trust funds achieve 100% efficiency and 5 unit trust funds pass the 0.9 scale, which are Eastspring Investments Growth Fund, Kenanga Ekuiti Islam Fund, PMB Shariah Tactical Fund, and AmDividend Fund. Finally, PMB Shariah Index Fund and KAF Dana Adib have the lowest rank in the BCC-I model, reaching the 0.8 scale. ![](6118a98417a44_media/media/image3.png) > **Figure 3**: Graph overall performance of unit trust funds BCC-I model Table 2 is the rank result comparison for CCR-I and BCC-I models. F1, F3, etc in the column DMU represent the 20 unit trust funds included in this study (refer Table 1). **Table 2**: Rank result comparison of CCR-I and BCC-I models. | CCR-I MODEL | BCC-I MODEL | | | | | | ----------- | ----------- | -------- | ------- | --------- | -------- | | DMU | **Score** | **Rank** | **DMU** | **Score** | **Rank** | | F1 | 1 | 1 | F1 | 1 | 1 | | F3 | 1 | 1 | F2 | 1 | 1 | | F7 | 1 | 1 | F3 | 1 | 1 | | F15 | 1 | 1 | F7 | 1 | 1 | | F13 | 0.9565 | 5 | F8 | 1 | 1 | | F16 | 0.9144 | 6 | F11 | 1 | 1 | | F2 | 0.8995 | 7 | F12 | 1 | 1 | | F4 | 0.881 | 8 | F13 | 1 | 1 | | F10 | 0.8693 | 9 | F15 | 1 | 1 | | F9 | 0.8468 | 10 | F17 | 1 | 1 | | F6 | 0.8442 | 11 | F18 | 1 | 1 | | F12 | 0.8252 | 12 | F19 | 1 | 1 | | F5 | 0.8236 | 13 | F20 | 1 | 1 | | F20 | 0.8005 | 14 | F10 | 0.9452 | 14 | | F11 | 0.7793 | 15 | F16 | 0.9417 | 15 | | F14 | 0.7501 | 16 | F4 | 0.928 | 16 | | F17 | 0.6354 | 17 | F6 | 0.9164 | 17 | | F8 | 0.0002 | 18 | F14 | 0.9146 | 18 | | F18 | 0.0002 | 18 | F5 | 0.8911 | 19 | | F19 | 0.0002 | 18 | F9 | 0.8807 | 20 | **CONCLUSION & RECOMMENDATIONS** In conclusion, this research has found that Islamic funds have the best performance than conventional funds since three Islamic funds consistent maintained the maximum level of efficiency with a score of 100% for both models compared to conventional funds with only one fund which had its remain rank and efficiency unchanged. These findings do not concur with Majid & Maulana (2012). Although, this study does display similar outcome with Taufiq et al. (2019). This could potentially be due to the period under investigation is different. The primary function of DEA for both CCR-I and BCC-I models find the optimal weighted data and slack analysis for input and output to achieve the lowest efficiency of each DMU (unit trust funds). The study has successfully achieved the objective of this study, which was to compare the performance of unit trust funds between conventional and Islamic funds using data envelopment analysis. The input and output were tested using both the CCR-I and BCC-I models of DEA. It is recommended that future studies include additional data, such as time series data for each unit trust fund in order to find better input and output, such as unsystematic risk and return, respectively. This type of data has such a strong historical series that it is simple to transform, clean, and vary in application. However, for research purposes, this type of data can be difficult to come by, particularly for unit trust funds. **REFERENCES** Bashir & Nawang, W. (2011). Islamic and conventional unit trusts in Malaysia : a performance comparison. *Journal of Islamic Economics, Banking and Finance*, *7*(4), 9–24. Hassan, A., Chachi, A., & Munshi, M. R. (2020). Performance measurement of Islamic mutual funds using DEA method. *Journal of Islamic Accounting and Business Research*, *11*(8), 1481–1496. https://doi.org/10.1108/JIABR-04-2018-0053 Ji, A., Liu, H., Qiu, H. J., & Lin, H. (2015). Data envelopment analysis with interactive variables. *Management Decision*, *53*(10), 2390–2406. Majid, A. & Maulana, (2012). A comparative analysis of the productivity of Islamic and conventional mutual funds in Indonesia: Data envelopment analysis (DEA) and general least square (GLS) approaches. *Gadjah Mada International Journal of Business*, *14*(2), 183–208. https://doi.org/10.22146/gamaijb.5439 Morningstar. (2020). *Unit Trust Funds Data Risk and Return*. Morningstar Malaysia. https://my.morningstar.com/my/ Rubio, J. F., Hassan, M. K., & Merdad, H. J. (2012). Non-parametric performance measurement of international and Islamic mutual funds. *Accounting Research Journal*, *25*(3), 208–226. https://doi.org/10.1108/10309611211290176 Saad, N. M., Majid, M. S. A., Kassim, S., Hamid, Z., & Yusof, R. M. (2010). A comparative analysis of the performance of conventional and Islamic unit trust companies in Malaysia. *International Journal of Managerial Finance*, *6*(1), 24–47. https://doi.org/10.1108/17439131011015779 Taufiq, M., Natasah, N. A., Qomariah, N., Sari, M. I., Budiarti, D. A., Rumintang, A. G., Azhari, M., Arif, M., Samim, M., Khurshid, M., Ali, A., Alsharif, S., Ahmad, Shabbir and Alsharif, D., Lestari, W. R., & Fajar, N. (2019). Islamic Versus Conventional Mutual Funds Performance in Pakistan; Comparative Analysis Through Performance Measures and DEA Approach. *Jurnal Ekonomi Dan Keuangan*, *2*(1), 1428. **APPENDIX** **3 YEARS, MONTHLY ENDED 31 MARCH 2021, UNIT TRUST FUNDS TRAILING DATA FOR ELEMENTS OF RISK (VOLATILITY) AND TOTAL RETURN RETRIEVE FROM MORNINGSTAR MALAYSIA OFFICIAL WEBSITE** | | | **Inputs** | **Output** | | | | | | ------------- | ---------------------------------- | ---------- | ---------- | ----------------- | ---------------- | ---------------------- | ------------------ | | **Funds No.** | **Funds Name** | **Alpha** | **Beta** | **R2** | **Sharpe Ratio** | **Standard Deviation** | **Total Return %** | | F1 | Apex Dana Aslah | \-5.06 | 0.83 | 64.55 | 0.31 | 16.25 | 6.80 | | F2 | Affin Hwang Aiiman Growth Fund | 7.65 | 0.78 | 82.85 | 0.51 | 17.14 | 10.80 | | F3 | BIMB i Growth Fund | 19.29 | 1.77 | 58.71 | 0.56 | 33.31 | 17.95 | | F4 | AmIslamic Growth | 2.31 | 1.04 | 82.93 | 0.12 | 16.43 | 3.71 | | F5 | KAF Dana Adib | 6.09 | 1.20 | 72.98 | 0.28 | 20.22 | 6.87 | | F6 | Kenanga Ekuiti Islam Fund | 5.47 | 1.08 | 78.62 | 0.29 | 17.48 | 6.82 | | F7 | Maybank Malaysia Growth-I Fund | \-0.68 | 0.83 | 87.87 | \-0.07 | 12.75 | 1.22 | | F8 | Phillip Dana Aman | \-1.94 | 1.22 | 81.37 | \-0.12 | 19.41 | \-1.27 | | F9 | PMB Shariah Index Fund | 4.82 | 1.16 | 91.49 | 0.25 | 17.52 | 6.12 | | F10 | PMB Shariah Tactical Fund | 8.63 | 1.07 | 73.38 | 0.46 | 17.95 | 10.14 | | F11 | Affin Hwang Equity Fund | 8.82 | 0.97 | 74.23 | 0.38 | 14.89 | 7.87 | | F12 | AmMalaysia Equity | 12.39 | 1.09 | 53.42 | 0.45 | 19.84 | 10.52 | | F13 | Apex Malaysia Growth Trust | 2.40 | 0.61 | 62.28 | 0.21 | 15.51 | 5.10 | | F14 | Eastspring Investments Growth Fund | 8.46 | 1.17 | 76.73 | 0.27 | 17.75 | 6.44 | | F15 | KAF Tactical Fund | 15.71 | 0.91 | 77.35 | 0.82 | 20.59 | 19.50 | | F16 | Kenanga Growth Fund | 3.35 | 0.78 | 78.46 | 0.25 | 17.57 | 6.00 | | F17 | Maybank Malaysia Growth Fund | 1.59 | 0.92 | 85.02 | \-0.10 | 13.22 | 0.75 | | F18 | Phillip Dividend Fund | \-2.72 | 1.09 | 85.63 | \-0.39 | 15.61 | \-4.37 | | F19 | RHB KLCI Tracker Fund | \-3.87 | 0.88 | 94.36 | \-0.55 | 12.04 | \-4.34 | | F20 | AmDividend Income | 11.01 | 1.05 | 60.26 | 0.43 | 17.99 | 9.48 |