# SIMULASI MATEMATIS OPTIMALISASI KOMPOSISI PROPORSI PORTOFOLIO SAHAM MENGGUNAKAN METODA OPTIMALITY LAGRANGE MULTIPLIER

## Authors

• Jarot Prasetyo UWD Klaten
• Anis Marjukah

## Keywords:

stock portfolio, expected results, stock portfolio risk, Lagrange Multiplier Optimality

## Abstract

This study aims to determine the composition of the proportion of funds (W) that should be invested in a stock portfolio. The method of determining it is using a simulation called the Optimization of the Optimization of the Share Portfolio Proportion Composition Using the Lagrange Multiplier Optimality Method. In this way it is expected that the proportion of funds provided by potential investors will be optimal so that the portfolios that are formed will be efficient, that is, at a certain level of risk, the portfolio will provide the maximum expected return; or at a certain level of expected return will result in minimal portfolio risk.

Through this simulation, several equations of the proportion of funds for each portfolio forming share will be generated. If the value of the expected return of each share is included in these equations, the proportion of funds generated will be optimal.

Using the stock data included in the LQ45 index of 15 types of stocks, the simulation produces an equation of the proportion for each type of stock at level E (Rp) of 0.014806, so a portfolio risk will be obtained of 6.50521E-17. This level of risk is much lower when compared to portfolio risk before using the ideal proportion, which is 0.00028591