The Comparison of Investment Portfolio Optimization Result of Mean-Variance Model Using Lagrange Multiplier and Genetic Algorithm

Investment portfolio optimization is carried out to find the optimal combination of each stock with the aim of maximizing returns while minimizing risk by diversification. However, the problem is how much proportion of funds should be invested in order to obtain the minimum risk. One approach that has proven effective in building an optimal investment portfolio is the Mean-Variance model. The purpose of this study is to compare the results of the Mean-Variance model investment portfolio optimization using Lagrange Multiplier method and Genetic Algorithm. The data used are stocks that are members of the LQ45 index for the period February 2020-July 2021. Based on the research results, there are five stocks that form the optimal portfolio, namely ADRO, AKRA, BBCA, CPIN, and EXCL stocks. The optimal portfolio generated by the Lagrange Multiplier method has a risk of 0.000606 and a return of 0.000726. Meanwhile, using the Genetic Algorithm resulted in a risk of 0.000455 and a return of 0.000471. Thus, the Genetic Algorithm method is more suitable for investors who prioritize lower risk. Meanwhile, the Lagrange Multiplier method produces a relatively higher risk, making it less suitable for investors who expect a small risk.