Optimizing the LQ45 Stock portfolio using Piecewise Linear Function: A Case Study from an Investor's Point of View

Abstract

In optimization problem solving, both linear and nonlinear approaches can be used, with nonlinear programming considering constraints or not. One effective method of nonlinear programming is the Piecewise Linear approach, which breaks down complex nonlinear functions into straight-line segments to make their solution easier. This method can be applied in the financial sphere, such as in stock investment. This study discusses the application of piecewise linear function in optimizing investment portfolios in Bank Jago Tbk. (ARTO), Barito Pacific Tbk. (BRPT), and Go To Gojek Tokopedia Tbk. (GOTO) stocks. The purpose of this study is to provide insight that Piecewise Linear can provide optimal solutions in managing investment portfolios by calculating the risks and returns of selected stocks. The results showed a risk with a level ???? as big as 0.01, the expected profit from the investment of the three stocks in the calculation period reached IDR 1,803,109. On the other hand, for investors who are more cautious and have a Level ???? as big as 1, the anticipated profit in the same investment is around IDR 1,275,052.