Optimasi Portofolio Saham pada Model Mean-Variance dengan Menggunakan Pengali Lagrange Berbasis Risk Appetite

Putra, Rakha Rahmadika (2025) Optimasi Portofolio Saham pada Model Mean-Variance dengan Menggunakan Pengali Lagrange Berbasis Risk Appetite. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Jumlah investor ritel di pasar modal Indonesia mengalami peningkatan pesat, tetapi masih banyak yang belum memahami cara menyusun portofolio investasi yang optimal. Penyusunan portofolio sering kali tidak mempertimbangkan tingkat risiko yang bersedia ditanggung oleh investor (risk appetite), sehingga berpotensi menimbulkan keputusan yang kurang tepat secara finansial maupun psikologis. Model Mean-Variance Markowitz dengan metode pengali Lagrange digunakan dalam penelitian ini untuk menentukan bobot optimal portofolio secara analitik. Pemilihan metode dilakukan karena mampu menangani batasan eksplisit seperti total bobot dan minimum pengembalian, serta menghasilkan solusi simbolik yang dapat ditelusuri secara matematis. Formulasi umum bobot optimal dikembangkan dan diuji menggunakan data historis saham dari Bursa Efek Indonesia. Dua skenario dibandingkan: model tanpa batasan dan model dengan batasan risk appetite berupa minimum dan maksimum alokasi tiap aset. Penerapan batasan menghasilkan portofolio dengan distribusi bobot yang lebih merata dan mencerminkan preferensi risiko investor, meskipun disertai peningkatan nilai risiko secara keseluruhan. Dampak penerapan batasan lebih terlihat pada portofolio tiga aset, di mana dominasi satu aset berhasil ditekan, sehingga struktur portofolio menjadi lebih seimbang. Hasil menunjukkan bahwa pendekatan ini tidak hanya memberikan efisiensi secara matematis, tetapi juga relevansi praktis dalam mencerminkan karakteristik dan kenyamanan risiko investor.
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The rapid growth of retail investors in Indonesia’s capital market has not been matched by a solid understanding of how to construct optimal investment portfolios. Many investors make allocation decisions without considering the level of risk they are willing to tolerate (risk appetite), which may lead to ineffective investment outcomes. This study proposes a solution using the Mean-Variance Markowitz model combined with the Lagrange Multiplier method to analytically determine optimal portfolio weights. The method is capable of handling explicit constraints, such as total weight and minimum return, while also allowing symbolic derivation that is mathematically transparent. A general formulation of optimal weights is derived and tested using historical stock data from the Indonesia Stock Exchange to estimate returns, variances, and covariances. Two scenarios are examined: an unconstrained model and a model constrained by risk appetite in the form of minimum and maximum asset allocations. The constrained model produces more balanced and realistic asset distributions, despite a slight increase in overall portfolio risk. The impact is especially notable in multi-asset portfolios, where excessive concentration is effectively reduced. Results indicate that the proposed approach is both mathematically efficient and practically relevant, aligning well with investor risk preferences in constructing efficient portfolios.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Optimisasi Portofolio, Mean-Variance, Pengali Lagrange, Risk Appetite, Batasan Efisien, Portfolio Optimization, Lagrange Multiplier, Efficient Frontier
Subjects:	H Social Sciences > HG Finance > HG4915 Stocks--Prices Q Science > QA Mathematics > QA401 Mathematical models.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Rakha Rahmadika Putra
Date Deposited:	04 Aug 2026 07:19
Last Modified:	04 Aug 2026 07:19
URI:	http://repository.its.ac.id/id/eprint/125309

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