Markowitz Model in The Analysis of Optimal Portfolio Establishment on Jakarta Islamic Index (JII) in Indonesian Stock Exchange

This study aims to know the optimal portfolio establishment using Markowitz model on Jakarta Islamic Index (JII) stocks in the period of December 2013-May 2019. The population of this study consisted of the company stocks on Jakarta Islamic Index (JII) in the period of December 2013-May 2019, and there were 59 stocks. While the study sample consisted of 14 company stocks and selected based on purposive sampling method. Data collection used in this study using documentation. Data analysis used in this study using the stages of Markowitz model and started collecting the close price until an optimal portfolio establishment. The result of this study showed that there were 8 company stocks included in the optimal portfolio. Namely AKRA (5,01%), ICBP (9,92%), INDF (3,75%), SMGR (8,61%), TLKM (29,01%), UNTR (20,30%), UNVR (20,88%), WIKA (2,53%). The expected return of the portfolio of 0,84%. Therefore, portfolio risk of 3,16%and smaller than the risk of individual stocks in the research sample.

INTRODUCTION the investment's awareness and literacy of sharia stocks in Indonesia are still minimal. According to data from the Indonesia Stock Exchange (2018) sharia stocks does not against Islamic principles or Islamic principles in the capital market in terms of capital participation.
One of the famous Islamic stock indexes in Indonesia is Jakarta Islamic Index (JII). According to Hartono (2017) Jakarta Islamic Index (JII) is one of Indonesia's sharia stock indexes which contains 30 stocks shariah with an average value of the largest capitalization. Table 1 will show the development of the index and market capitalization of Jakarta Islamic Index (JII) in the period of December 2013-May 2019. Based on table 1, can be seen the development of index and market capitalization on Jakarta Islamic Index (JII) in the period of December 2013-Mei 2019 is fluctuate. Generally, almost all stocks on Jakarta Islamic Index (JII) are included in large-capitalization or blue chip in Indonesia Stock Exchange and relatively safe, but the price of blue-chip stocks is also relatively expensive. The price of Jakarta Islamic Index (JII) stocks tends to fluctuate and because of that, market capitalization also fluctuates. In addition, stock risks are also uncertain so that an optimal portfolio establishment is important to help the investors for making good investment decisions. One of the optimal portfolio establishment models to predict good returns with low risks is Markowitz model.
Markowitz in his article entitled The Journal of Finance (1952) states that there is a portfolio that provides maximum expected return and minimum variance. In addition, diversification cannot eliminate all variance. The Portfolio with the maximum expected return is not to be with minimum variance. There is a rate that is an investor can obtain expected return by taking the variance and also reduce the variance with a certain return. In addition, Lee et al., (2015) stated that Markowitz model tries to reduce the total variance of portfolio returns by combining different assets (diversification) whose returns are not perfectly positively correlated. According to Boangmanalu and Komalasari (2015) Markowitz's theory has an advantage that investors can use information maximally in choosing portfolios through efficient set observations from the calculation of risk, correlation and covariance of stocks.
Yunita (2018) conducted a study determining the optimal stock portfolio with Markowitz model (case studies on Jakarta Islamic Index (JII) in the period of May 2013-March 2018) and the total sample consisted of 29 stocks. That study also used non-purposive sampling. The results of this study showed that there were 10 stocks included in the optimal portfolio, namely AKRA, ADRO, ICBP, INCO, MYRX, PTPP, PWON, TPIA, UNTR, UNVR. In addition, Yuana, et al., (2016) also conducted a study determining the optimal stock portfolio with Markowitz model (studies on Jakarta Islamic Index (JII) in Indonesia Stock Exchange in the period of June 2013-November 2015). A total sample of that research consisted of 19 stocks from 40 stocks.
The results of the study showed that there were 7 stocks included in the optimal portfolio. Namely, WIKA, AALI, AKRA, ICBP, KLBF, UNTR, and UNVR.
The previous research has a difference with the research that will be developed at this time that is the previous research has a shorter time. Yunita's (2018) research conducted for 59 months and Yuana's et al. (2016) research conducted for 30 months, while the research that will be developed at this time is conducted for 66 months and starting from the period of December 2013-May 2019. In addition, the technical sampling in Yunita's research (2018) was different from the research that will be developed at this time by using a purposive sampling method. Based on the background and various previous studies, then the optimal portfolio establishment with Markowitzmodel is important to develop and can help investors to maximize the level of return for certain risks, or minimize risk for certain levels of return.

Source: Indonesia Stock Exchange(2018)(data processed)
The variable used in this study is Markowitz model in optimal portfolio establishment. The operational definitions and measurement variables as follows: Realized return is the level of profit of each company stock on Jakarta Islamic Index (JII) or actual return earned in the period of December 2013-May 2019. According to Hartono (2017), the realized return can be calculated with the total return and the formula as follows:Stock Returns = The expected return (expected return) of the stock is the level of return or profits that investors expect on Jakarta Islamic Index (JII) in the future. According to Hartono (2017), expected return formula as follows: Covariance is a measure that can show the directional between two variables. According to Hartono (2017) The correlation coefficient shows the relationship between two variables with each deviation on Jakarta Islamic Index (JII). According to Hartono (2017), the correlation coefficient formula as follows: rAB = ρAB = The Portfolio risk is a return variance of securities on Jakarta Islamic Index (JII) that can establish the portfolio. According to Hartono (2017), the formula for variance and standard deviations as follows: σp² = w1 2 σ1 2 + w2 2 σ2 2 + 2.w1. w2. σ12 variance-covariance matrixfor n-assetsas follows: The lowest return obtained by Perusahaan Gas Negara (Persero) Tbk. (PGAS) with the realized return of -0.32590 or -32.59%and the expected return of -0.00494 or -0.449%. Based on table 3, Perusahaan Gas Negara (Persero) Tbk stock (PGAS) had a negative realized return and expected return which is the company obtain capital loss (loss) and Perusahaan Gas Negara (Persero) Tbk (PGAS) stock is not included in the next calculation because it will produce a negative portfolio expectations.

Covariance between two stocks in a portfolio
Based on the covariance matrix that obtained 161 stock combinations with a positive value from 169 stock combinations and which is the combination of the two stocks in a portfolio tends to move in the same direction. In addition, the covariance matrix also obtained eight negative stock combinations, namely AKRA-TLKM, ICBP-UNTR, INDF-UNTR, SMGR-TLKM, SMRA-UNTR, TLKM-UNTR, TLKM-WIKA, and UNTR-UNVR. Thus, these stocks move in the opposite direction and if one stock has an increase in return, then the other stock has a decrease in return. The covariance matrix between the two shares is shown in table 5:

Correlation Coefficient Between Company Stock Prices
Based on the correlationcoefficient matrix that the correlation between the same stock is +1. Which means that all the risks cannot be diversified. In addition, the correlation between the different stock is between +1 and -1. This means that all stocks of a company that are included in the research sample can be diversified or will reduce the risk by forming various types of stocks in a portfolio. It can be seen that the portfolio will reduce the risk, but not eliminate all the risks. The correlation coefficient matrix is shown in table 6.

Determine the Proportion of Funds for Each Stock, Expected Return and Risk of the Portfolio
Before looking for an optimal portfolio, it is necessary to know the combinations of efficient portfolios in the research sample to provide an overview of efficient portfolio combinations, so that investors can make these combinations as a reference in investment decisions. Based on the efficient set graph in figure 1, the MAX, MVP points, and point 1 to point 26 are the efficient sets of Jakarta Islamic Index (JII) stocks which are the research sample. The MAX value indicates the highest standard deviation and expected returns on an efficient set for the highest deviation assets. The MVP (minimum variance portfolio) value is the smallest standard deviation value and expected returns on an efficient set for the smallest deviation asset. Next will be made 26 portfolios from 13 research sample stocks by forming the efficient set from the smallest standard deviation to the highest standard deviation with the same interval. Thus points 1 to point 26 show the efficient set of standard deviation values and the efficient expected return of portfolio values. The efficient graph set that forms an efficient portfolio on the research sample shown in figure 1.

Source: The Results of data analysis using Microsoft Excel
After looking for an efficient graph set, the next step is to calculate the optimal portfolio formation by using the solver program on Microsoft Excel.  Table 7 shows that from 13 stocks which are included in the category of an optimal portfolio, only 8 stocks that included in an optimal portfolio with the smallest proportion of portfolio risk. This is influenced by various factors such as realized return, expected return, standard deviation, covariance, and the correlation coefficient between stocks. In addition, in figure 2 it can be known that WIKA stocks have the smallest proportion of 2.53%. This is because based on the calculations obtained that WIKA stocks occupy the highest expected return and expected return from 14 stocks the research sample of 0.87332 and 0.01323. In addition, WIKA stocks also occupy the second position with the biggest risk that is 0.12063.
Based on the proportion of funds from company stocks obtained that the expected return of a portfolio of 0.84%with a portfolio risk of 3.16%. The portfolio risk is smaller than the individual risk of Jakarta Islamic Index (JII) stocks which are included in the research sample. For more details can be seen in

Source: The Results of data analysis using Microsoft Excel
The results of the study can prove that diversification in Markowitz model can reduce the variance with certain returns. Thus, the proportion of funds, expected return of portfolio and portfolio risk are the best projection based on results obtained and can be used by investors in choosing optimal stocks for investment. Based on the results, Markowitz model is very suitable for novice investors who are likely to want a certain profit with the smallest risk. In addition, Markowitz model is very suitable for investors who are not likely a risk (risk-averse).

CONCLUSIONS AND SUGGESTIONS Conclusions
Based on the optimal portfolio analysis by using Markowitz model on Jakarta Islamic Index (JII) stocks in the period of December 2013-May 2019 obtained 8 stocks that included in the optimal portfolio. The proportion of the stocks on an optimal portfolio which consists of AKRA of 5.01%, ICBP of 9.92%, INDF of 3.75%, SMGR of 8.61%, TLKM of 29.01%, UNTR of 20.30%, UNVR of 20.88%, and WIKA of 2.53%.
The proportions of each stock are different because of different stock prices, expected returns, risks, and covariance between stocks. Based on the proportion of funds from each stock on optimal portfolio obtained expected return of a portfolio of 0.84%with a portfolio risk of 3.16 %. The amount of portfolio risk was smaller than all the risk of individual stocks that were included in the sample observation. In addition, the expected return of the portfolio was not too different from the expected return of an individual stock. Thus, Markowitz model can be proven that diversification can reduce the investment risk of stocks with a certain rate of return.

Suggestions
Based on the calculation of the results, the advice that can be given for further study is to further develop this study by providing an analysis of the latest period investment stocks with a longer observation period. In addition, the next researcher is also expected will be able to analyze Markowitz model with optimal portfolios based on investor risk preferences and will explain other sharia stock indices.
Investors who are likely to invest in Jakarta Islamic Index (JII), especially investors who are not likely a risk, should be chosen optimal stocks with the proportions that already exist in this