Available online at https://ejournal.corespub.com/index.php/ijmsc/index International Journal of Mathematics, Statistics, and Computing Vol. 2, No. 1, pp. 9-15, 2024 e-ISSN 3025-0803 Multiobjective Optimization of Stock Portofolio Rini Cahyandari 1* , Susan Kamelia 2 , Volodymyr Rusyn 3 1,2 Department of Mathematics, Faculty of Science and Technology, UIN Sunan Gunung Djati Bandung 3 Yuri Fedkovych Chernivtsi National University, Kotsyubynsky str., 58012 Chernivtsi, Ukraine *Corresponding author email: rini_cahyandari@uinsgd.ac.id Abstract Diversification is a method used to reduce risks by allocating several financial, industrial, and other instruments. Investors might need to use this method to allocate their companies’ funding as efficient as they should be. Mean variance portfolio is a diversification theory designated for investors who are aware of potential risks. On the other hand, multi-objective portfolio optimization is another theory that suits for investors who are more unaware, or choose to neglect potential business risks. Multi- objective optimization can boost source of income and minimize the risks while utilizing k weighting coefficient as risk aversion index. This research aims to form an optimal portfolio from each perspective of selected investors using multi-objective optimization, as well as to analyze the benefits and risks that the investors will have. Samples used in this research are sharia stocks actively involved in Jakarta Islamic Index (JII) and non-sharia stocks which are actively involved in LQ-45 from January 2013 to January 2018. Keywords: Diversification, multi-objective optimization, optimal portfolio 1. Introduction Statistics is a part of mathematics that specifically discusses ways of collecting, analyzing and interpreting data. In other words, the term statistics is used to denote a body of knowledge about methods of sampling (data collection), as well as analysis and interpretation of data (Lock et al., 2020). With statistics, you can explain the relationships between variables, make better decisions, overcome changes that occur and make plans and forecasts. Statistics is widely applied in various sciences, ranging from social sciences to the business sector. One of the uses of statistics in the economic field is determining the risk and return of a portfolio in determining investment in the capital market. The capital market is a means of funding for companies and governments, and as a means of investment activities for fund owners (Black & Gilson, 1998). Thus, the capital market facilitates various facilities and infrastructure for buying and selling activities and other related activities. The capital market has a big role in a country's economy because the capital market carries out two functions at once, namely the economic function and the financial function (Stulz, 2001). In conditions of a financial system where the level of volatility is considered high, the sharia financial system, especially the sharia capital market, offers an attractive alternative compared to the conventional industry which still relies on usury as its basic foundation. According Dixit & Pindyck (1994), investment can be interpreted as a commitment to invest a certain amount of funds now with the aim of obtaining profits in the future. Investment can relate to investing a certain amount of funds in real stocks such as: land, gold, houses and other real stocks or in financial stocks such as: deposits, stocks, bonds and other securities (Siegel, 2021). Securities traded on the Indonesian capital market in the form of equity are stocks, both ordinary stocks and preferred stocks as well as evidence of rights and warrants. Of the four equity securities, ordinary stocks are the most important and best known securities by the Indonesian people. Therefore, the term equity market is often understood as the stock market and the term stocks are often meant to mean ordinary stocks. Once issued, equity securities can be traded by investors on the stock exchange. Currently in Indonesia there is one stock exchange, namely the Indonesian Stock Exchange (BEI). Investing in risky stocks such as stocks will not only generate profits (returns) but also have to face losses (risk). The rate of return can be measured from expected return while risk can be measured from variance or standard deviation. Therefore, diversification is needed to reduce risk. Professor Harry Markowitz is the originator of portfolio diversification theory, which became known as Markowitz's diversification theory. Markowitz's efficient portfolio