Investment Portfolio Optimization Model Using The Markowitz Model

Abstract

The stock portfolio is related to how someone allocates several shares in various types of investments so that the results achieve maximum profit. By implementing a diversification system or portfolio optimization on several stocks, investors can reduce the level of risk and simultaneously optimize the expected rate of return. This study aims to determine which stocks listed on the Indonesia Stock Exchange (IDX) and included in the portfolio for the 2021-2022 period are eligible to be included in the optimal portfolio and to determine the proportion of funds for each share in the formation of the optimal portfolio. The population in this study are all shares included in the Indonesia Stock Exchange (IDX) listed on the Indonesia Stock Exchange (IDX) for the 2021-2022 period. The sample of this research is five stocks that are candidate portfolios. The sampling method uses a purposive sampling method with the criteria of 5 stocks with the highest positive ratio. The population in this study was all 30 companies included in the IDX30, while the samples were five companies. Data were analyzed using a mean-variant optimization model with a research duration between May 2021 and May 2022. Based on the results of the investment portfolio optimization analysis on the 5 (five) selected stocks, this study shows that, out of 23 stocks, five stocks are eligible to enter the optimal portfolio with their respective proportions, namely PT Adaro Energy Indonesia Tbk (ADRO) 20%, PT Astra International Tbk (ASII) 26%, PT Merdeka Copper Gold Tbk (MDKA) 10%, PT XL Axiata Tbk (EXCL) 19%, PT Bukit Asam Tbk (PTBA) 25%. The portfolio of these stocks generates an expected return of 0.00217 at a risk level of 0.00022. It is hoped that this research can be helpful to add to the literature on investment optimization models, especially the concentration of Mathematics in Finance, and serve as an additional reference for further research, as well as an alternative for investors in optimizing investment portfolios.

Modeling of Mean-Value-at-Risk Investment Portfolio Optimization Considering Liabilities and Risk-Free Assets

“…It means that the greater the risk aversion of the investor, the smaller the mean of the portfolio return becomes and vice versa. It is logical because if investors avoid uncertainty (this means they have high-risk aversion), the mean of the portfolio return that may be obtained is also very small [39,40].…”