Optimal Portfolio Analysis with Solver Application in Wetland Plantation Subsector

Investments made by investors should submit to a Markowitz portfolio, where the goal is to get an optimal portfolio investment from several existing stocks. The goal of a portfolio is to maximize stock returns and minimize risk. The object of this study is plantation sub-sector companies listed on the IDX for the 2018-2022 period. The population is 19 companies in the plantation sub-sector, while the sampling method is 6 companies using purposive sampling. Through this research, investors are expected to be able to see which stock portfolio is the most optimal of several efficient portfolios in the agricultural sector. In addition, the plantation sub-sector supports government programs on food security for industry and consumers and increases non-oil and gas income, and increases the income of all relevant stakeholders, which in turn can increase the income and welfare of the Indonesian people. 
 


Introduction
Plantations have an important and strategic role in national development, especially in increasing the prosperity and welfare of the people, earning foreign exchange, providing employment, obtaining added value and competitiveness, meeting domestic consumption needs, domestic industrial raw materials, and optimizing resource management. Nature in a sustainable manner. The plantation subsector is an expected sector by the government in order to contribute to the gross domestic product (GDP), which continues to increase every year.
Over the past five years, the growth rate of production, exports, and consumption of palm oil has tended to increase, especially production and consumption. However, exports have decreased slightly from 2020 to 2022 due to the 2020 COVID outbreak. It is bright for investors if they have shares in the plantation sub-sector so that they become the target of investors and potential investors in the capital market in Indonesia. The plantation sector also contributes to state revenue ( GDP ) for the country (Katadata.co.id, 2023). In forming a portfolio, investors always want to maximize the expected return with a certain risk they are willing to bear or look for a portfolio that offers the lowest risk with a certain return, in line with (Indrayanti, 2013;Nurdianingsih, 2021). This characteristic of a portfolio is referred to as an efficient portfolio. The portfolio that an investor chooses from among the many choices in an efficient portfolio is called the optimal portfolio (Tandelilin, 2010).
Investments made by investors should submit to a Markowitz portfolio, where the goal is to get an optimal portfolio investment from several existing stocks. The goal of a portfolio is to maximize stock returns and minimize risk. The object of this study is plantation sub-sector companies listed on the IDX for the 2018-2022 period. The population is 19 companies in the plantation subsector, while the sampling method is 6 companies using purposive sampling. Through this research, investors are expected to be able to see which stock portfolio is the most optimal of several efficient portfolios in the agricultural sector. In addition, the plantation subsector supports government programs on food security for industry and consumers and increases non-oil and gas income, and increases the income of all relevant stakeholders, which in turn can increase the income and welfare of the Indonesian people.

Open Access Indonesia Journal of Social Sciences
Formation of the optimal portfolio can be done in several models, one of which is the Markowitz Model.
The Markowitz model is a method for forming an optimal portfolio by considering various information regarding the characteristics of each security to be included in the portfolio (Tandelilin, 2010). The purpose of the investment portfolio is to reduce the risks faced by investors according to the investor's return and risk preferences.
This research is in line with (Anam, 2021), the title of the analysis of determining the optimal portfolio on the Jakarta Islamic Index, which is listed on the Indonesian stock exchange, where the result is that the analysis of forming an optimal portfolio using the Markowitz model is able to produce 6 (six) candidates stocks as a constituent of the optimal portfolio, while in research (Avianti, 2021), analysis of optimal portfolio formation with the single index model and Z-Score on IDX BUMN 2O Issuers, that the analysis results from the single index method have a portfolio return of 0.001339 with the risk that must be faced is 0.0037724. The z-score growth investing method obtains a portfolio return value of 0.000989 and has a risk of 0.023369. Also in line with research (Dewi, 2020;Yunita, 2018), formation of an optimal portfolio on IDX80 index stocks using the Markowitz model.
This study aimed to present portfolio data of the plantation sub-sector in wetlands.

Investment
According to Jones in investment, investment can be defined as a commitment to activity in placing funds in one or more assets over a certain period.

Definition portfolio
The investment decision process is a continuous process (going process) that includes five decision stages such as determining investment objectives, determining investment policies, selecting portfolio strategies, selecting assets, and measuring and evaluating portfolio performance. Investors can choose to invest their funds in various assets, both risky, risk-free or a combination of the two. A risky asset is an asset whose return rate in the future still contains uncertainty. A risk-free asset is an asset whose future rate of return can be ascertained at this time and is indicated by a return variance equal to zero. One example of a risk-free asset is a Bank According to (Copeland, 2005), portfolio theory is a modern theory regarding decision-making in The efficient portfolio then differs from the optimal portfolio. The optimal portfolio is the portfolio chosen by an investor from the many choices that exist in a collection of efficient portfolios. The portfolio that will be selected is related to the preference of the concerned investor regarding the returns and risks that will be borne.

Concept of risk and return
Portfolio risk is a variant of the return on assets formed in a portfolio. According to (Hartono, 2003), stated that the measure of risk is seen from the standard deviation. Mathematically, the formula for calculating the standard deviation is written as follows: Investors can diversify in several ways, namely by forming a portfolio containing many assets, forming a random portfolio, or diversifying using the Markowitz method (Hartono, 2003).

Diversify a lot of assets
The laws of statistics say that the larger the sample size, the closer the sample mean is to the expected value of the population. This law is called the Law of large numbers. The assumption used in this diversification is that the rate of return (rate of return) for each security is statistically independent. This means that the rate of return for one security is not affected by the rate of return for other securities.

Diversify by random
Random diversification is the formation of a portfolio by choosing securities at random without regard to the characteristics of the relevant investments. Investors simply select securities at random.

Diversification Markowitz
Mean-variance method of Markowitz using securities that have a correlation smaller than +1 will reduce the risk of the portfolio. The more securities that are included in the portfolio the smaller the risk of a portfolio.

Methods
The object of this research is to use plantation sub-

Results and Discussion
The results of this study include the process of forming an optimal portfolio for sectoral stocks for the   Table 3 shows the results of calculating the proportion of funds using the variance-covariance matrix. Then calculate the optimal proportion of funds using the Solver application in Microsoft Excel 2016, then the expected return portfolio will be calculated from the portfolio risk from the optimal proportion of funds.   Table 5 shows that there are 6 company shares that are included in the optimal portfolio, DSNG shares have a value of 32.44% and the lowest value is owned by SIMP shares of 1.69%. Table 6. Expected return portfolio at the same and optimal proportion of funds.
Expected return portfolio Equal fund proportion 10.14% Optimal fund proportion 14.16% Table 6 shows different results. For the same proportion of funds, it produces an expected portfolio return of 10.14%, while for the optimal proportion of funds with the help of solver, it produces an expected return of 14.16%. Meaning that the expected is much higher than the expected return of a portfolio that only uses the same proportion of funds. Table 7. Portfolio risk in equal and optimal proportion of funds.
Portfolio risk Equal fund proportion 24.28% Optimal fund proportion 24.05% After using the software solver, the reduced risk factor can be seen in Table 7, which shows different results, namely that the risk of a portfolio with an optimal proportion of funds decreases compared to using the same proportion of funds, which is 24.05% compared to the risk with the same proportion of funds, which is 24.28%. This means that the risk of the portfolio using the optimal proportion of funds with the help of solver software is reduced because the portfolio is carried out using the Markowitz portfolio approach.
The results of this study of the 6 optimal portfolio candidates turn out to be all stock candidates that can  (Mahayani, 2019;Sari, 2020).

Conclusion
It turns out that after optimizing the weight of funds with a solver application on plantation sector stocks. It turned out that all of the samples of plantation sector companies, namely the 6 companies, were included in the optimal portfolio category.