Analysis of Optimal Portfolio Comparison on Shares of Sri Kehati by using Single Index Model and Random Model

The purpose of this study is to provide empirical evidence that the determination of a stock portfolio using a single index model can provide optimal returns compared with the determination of stock portfolio using a random model. The sample in this research is 25 shares joined in SRI-KEHATI selected using purposive sampling. The data analysis technique used the average test for two independent samples (Mann Whitney Test (U Test)). The results showed that the determination of the stock portfolio using a single index model can provide optimal return compared to the determination of the stock portfolio using random model.

This is caused by differences in internal factors (management, marketing, and competitive ability) and external factors (government policies, social security, culture, defense and security, competitors as well as people's tastes and purchasing power). In deciding an investment, investors pay attention to two important things, namely the return and risk of the investment. For securities that have the same return, investors will choose the lowest risk. As for securities that have the same risk, investors will choose a high return. With this stock diversification, it is hoped that it will reduce the level of risk. Diversification is done by means of a stock portfolio.
Alternative stock selection and portfolio determination can be done using various analytical tools, one of which is using a single index model. The single index model is widely used as an analytical tool to get an efficient portfolio, in addition to the simple model it is also easy to operate. Investors must be rational in dealing with the stock trading market. However, investors sometimes only follow individual desires, join in or gamble in determining portfolios. This is better known as random or random portfolio determination (without regard to the relevant investment characteristics).
This research refers to the research conducted by Henry Dwi Wahyudi (2002). Henry Dwi Wahyudi researches investment analysis and optimal portfolio determination on the Jakarta Stock Exchange. The study concluded that the determination of the portfolio using the Single Index Model can provide optimal returns compared to determining the portfolio randomly or randomly. Thus, an investor who wants to be involved in the capital market in buying and selling shares must leave the culture of joining in or gambling and so on which is irrational (as an investor, you must be rational in dealing with the stock buying and selling market). Meanwhile, research conducted by Susanti (2012) concluded that the determination of a portfolio using the Single Index Model can provide optimal returns and the resulting risk is smaller than the Random Model.Research conducted by Prastiwi (2006) shows that the return generated by determining the portfolio using the Random Model and Single Index Model shows that there is no difference in the expected return of the portfolio.

II. METHODS
The research instruments used in this study are:

III. RESULTS AND DISCUSSION Data Description Descriptive statistics
Descriptive statistics are statistics used to analyze data by describing or describing the data that has been collected as it is without intending to make conclusions that apply to the public or generalizations (Sugiyono, 2015: 147). Descriptive statistical tests are carried out to provide an overview or description of the observational sample of a data seen from the average value (mean), standard deviation, highest value, lowest value of each variable. The results of descriptive statistical analysis can be seen in Table 4.1 below: Based on Table 4.1, it can be seen that the portfolio return variable with a value of 20 has a minimum value of 0.00, a maximum value of 0.00, an average (mean) of 0.0010, and a standard deviation of 0.00096. While the variable for determining the portfolio with a value of n totaling 20 has a minimum value of 1, a maximum value of 2, an average (mean) of 1.50, and a standard deviation of 0.513.

Sample Selection
The sample selection was carried out by purposive sampling, namely permanent companies that were included in the SRI-Kehati index during the Research Period, namely May 2016 -April 2017 and these companies also had complete data during the research period from May 2016 to April 2017. The sample companies in this study can be seen in the Appendix.

Comparison of single index model and random model in calculation. a. Single Index Model
In this study, the portfolio that is a candidate for the single index model is a portfolio that has an ERb value greater than the Ci value (ERb > Ci). From the calculations that have been carried out, there are 10 portfolio candidates that meet the following criteria:

b. Random Model
The selection of a random model portfolio candidate is done with the help of the Microsoft Excel program with the "RAND" formula. This model allows each portfolio to have the same opportunity to become a candidate. Based on the selection of portfolios using a single index model, 10 portfolios were obtained, so the researcher will also choose 10 portfolios that will be used as candidates for the random model. The randomization of the portfolio which became the random model was obtained by the candidates as follows:

Hypothesis Testing Results
After analyzing stocks and obtaining candidate portfolios with single index models and random models, hypothesis testing will be carried out by comparing portfolio returns between stocks that are candidate portfolios using a single index model with stocks that are candidates for portfolio random models.
Hypothesis testing was carried out with the average test for two independent samples (Mann Whitney Test (U Test)). Before testing the hypothesis, the hypothesis can be formulated as follows: H0 : Determining a stock portfolio using a single index model can provide a non-optimal return compared to determining a stock portfolio using a random model. H1 : Determining a stock portfolio using a single index model can provide optimal returns compared to determining a stock portfolio using a random model.
The decision-making criteria in the Mann Whitney test (U Test) with a significance level of 0.05 are as follows: ∑ If Pvalue (Asymp. sig. (2-tailed)) < 0.05 then H0 is rejected ∑ If Pvalue (Asymp. sig. (2-tailed)) > 0.05 then H0 is accepted The following results of hypothesis testing using the SPSS program can be seen in the following table: The table above shows the Mean Rank or the average rank of each group. The first group (Single Index) has an average rating value of 13.20, which is greater than the average rating of the second group (Random) which is 7.80. The table above shows a U value of 23,000 and a W value of 78,000. When converted to a Z value, the amount is -2.044. The sig value or P Value is 0.041. It turns out that the P Value is less than the probability (0.041 < 0.05) then H0 is rejected, meaningDetermining a stock portfolio using a single index model can provide optimal returns compared to determining a stock portfolio using a random model.

Discussion
After testing the hypothesis, it is known that stock portfolio determination using a single index model can provide optimal returns compared to stock portfolio determination using a random model. The results of this study are in accordance with research conducted by Linda Ratna Sari (2015) examining the comparison of stock returns of Kompas 100 using a single index model and a random model showing that determining a stock portfolio using a single index model can provide optimal returns compared to determining a stock portfolio using a random model. . This research is also supported by research conducted by Ni Putu Nonik Hariasih and Dewa Gede Wirama (2016) with research results stating that there are differences in portfolio returns using a single index model and a random model. Determining the optimal portfolio using a single index model can provide a higher return than the random model portfolio.

IV. CONCLUSION
Based on the hypothesis testing that has been done on 20 stock portfolios by comparing the single index model with the random model, it can be concluded that the determination of the stock portfolio using the single index model can provide optimal returns compared to determining the stock portfolio using the random model.

V. ACKNOWLEDGMENTS
After analyzing and discussing the problems that occur, namely the use of a single index model and a random model in assessing risk and stock returns for the choice of investing in SRI-Kehati Index companies on the IDX, the suggestions that can be given are as follows: 1. The model used in this study is a single index model and a random model with daily closing prices. For further research, other models can be used such as non-linear models, mean variance models, goal programming models. And can add a test of the correlation between stocks in the formation of a portfolio.
2. In this study, using a sample belonging to the SRI-Kehati Index stock. It is likely to be taken into consideration in further research by using stocks other than the SRI-Kehati index, so that a larger number of samples can be obtained. 3. The stock sample used in this study is SRI-Kehati with an observation period from May 2016 to April 2017, for further research, data that is not only included in the SRI-Kehati calculation factor or can extend the research period.