Optimalisasi Portofolio Dengan Kendala Kardinal Dan Variabel Semi-Continuous Menggunakan Metode Outer Approximation

Kirana, Dea (2022) Optimalisasi Portofolio Dengan Kendala Kardinal Dan Variabel Semi-Continuous Menggunakan Metode Outer Approximation. Other thesis, Institut Teknologi Sepuluh Nopember Surabaya.

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Abstract

Investasi pada pasar modal memiliki tujuan untuk menghasilkan return yang maksimal dengan risiko yang minimal. Salah satu cara untuk mencapai tujuan tersebut adalah membentuk portofolio saham yang merupakan kumpulan dari beberapa aset saham pilihan. Pemilihan aset didasarkan pada data harga saham sebelumnya dari aset tersebut. Model Markowitz dapat membantu investor untuk menentukan proporsi dari aset-aset yang dipilih. Model Markowitz merupakan model sederhana yang dapat ditambahkan suatu kendala untuk membatasi risiko non-sistematis berbentuk kendala kuadratik. Selanjutnya ditambahkan kendala kardinal dan kendala semi-continuous pada model. Kendala kardinal membatasi banyaknya aset dalam portofolio, sedangkan kendala semi-continuous membatasi nilai proporsi aset. Penambahan kendala-kendala tersebut membentuk suatu model Quadratically Constraint Quadratic Program (QCQP) dengan kendala kardinal dan variabel semi continuous. Model Mixed Integer Quadratically Constrained Quadratic Program (MIQCQP) dari optimalisasi portofolio diselesaikan dengan membuat program pada software MATLAB menggunakan fungsi cplexmiqcp dari CPLEX. Selanjutnya model diselesaikan menggunakan metode Outer Approximation. Simulasi numerik dilakukan menggunakan sampel data saham dari 15 perusahaan yang bergerak di bidang teknologi. Hasil simulasi menunjukkan bahwa nilai objektif metode Outer Approximation 0,0021% lebih berisiko daripada cplexmiqcp. Return dari penyelesaian model menggunakan metode Outer Approximation lebih besar 0,0324% daripada return penyelesaian model menggunakan cplexmiqcp. Hal ini menunjukkan bahwa metode Outer Approximation dapat menyelesaikan permasalahan optimalisasi portofolio
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Investment in the capital market has a goal that is to generate maximum returns with minimum risk. This goal can be achieved by building a stock portfolio, which is a collection of selected different stock assets. The selection of assets is determined based on the data of the previous assets’ stock price. The Markowitz model can help investors to determine the proportion of selected assets. The Markowitz model is a simple model of portfolio selection in which a constraint can be added to limit the non-systematic risk in the form of a quadratic constraint. In addition, cardinal constraint and semi-continuous constraint will be added into the model. Cardinal constraint limit the number of assets in the portofolio, while semi-continuous constraint will limit the value proportion of selected assets. That constraints addition forms a Quadratically Constraint Quadratic Program (QCQP) model with cardinal constraint and semi-continuous variables. The Mixed Integer Quadratically Constrained Quadratic Program (MIQCQP) model of portfolio optimization will be solved by creating a program on MATLAB software using the cplexmiqcp function of CPLEX. Furthermore, the model was solved using the Outer Approximation method. Numerical simulations were running by using stock data samples from 15 companies in the technology industry. The simulation results show that the objective value of the Outer Approximation algorithm is 0.0021% more risky than cplexmiqcp. In addition, the expected return obtained from Outer Approximation method is 0.0324% greater than its from cplexmiqcp. This shows that Outer Approximation method can solve a portfolio optimization

Item Type:	Thesis (Other)
Additional Information:	RSMa 510.8 Kir o-1 2022
Uncontrolled Keywords:	Portofolio, Optimalisasi, Mixed Integer Quadratically Contraint Quadratic Program, Metode Outer Approximation
Subjects:	Q Science > QA Mathematics > QA371 Differential equations--Numerical solutions Q Science > QA Mathematics > QA372.B9 Differential equations--Numerical solutions. Runge-Kutta formulas--Data processing.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	EKO BUDI RAHARJO
Date Deposited:	13 Jan 2023 07:39
Last Modified:	13 Jan 2023 07:39
URI:	http://repository.its.ac.id/id/eprint/95388

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