BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application

INTEGRATION OF DAVIES-BOULDIN INDEX VALIDATION AND MEAN-VARIANCE EFFICIENT PORTFOLIO IN K-MEANS++ CLUSTERING FOR OPTIMIZATION OF THE LQ45 STOCK PORTFOLIO

Dhandio, David Jordy (Unknown)
Sulistianingsih, Evy (Unknown)
Satyahadewi, Neva (Unknown)



Article Info

Publish Date
01 Sep 2025

Abstract

Stock investment involves allocating funds to get returns based on the associated risks. In stock investments, returns and risks exhibit a linear correlation, meaning higher expected returns come with higher risks. Risk in stock investments can be minimized by forming portfolios using a cluster analysis approach, where the groups of stocks generated from the analysis represent the resulting portfolios. This research aims to form an optimal stock portfolio using K-Means++ Clustering, validated by the Davies Bouldin Index (DBI), the weighting of stocks in a portfolio using the Mean-Variance Efficient Portfolio (MVEP), and evaluated based on the Sharpe Index. The data used include stocks indexed in LQ45 from February 2020 to August 2024, stock closing prices from August 1, 2023, to August 1, 2024, company financial ratios as of June 2024, and the average Bank Indonesia interest rate from August 2023 to August 2024. Based on the financial ratios, K-Means++ Clustering and DBI validation identified three optimal clusters. Clusters 1 and 2, consisting of single stocks, cannot be directly utilized as portfolios due to the requirement for diversification. Each cluster’s stocks with the highest expected return were selected to form a new portfolio. According to the MVEP analysis, the investment proportion f each stock in portfolio 1 is 44.10% (BBCA.JK), 15.40% (BBNI.JK), 2.89% (BMRI.JK), 15.02% (CPIN.JK), and 22.60% (PGAS.JK). In portfolio 2, the weights are 27.68% (BBTN.JK), 36.00% (ADRO.JK), and 36.33% (BMRI.JK). Based on the Sharpe Index, portfolio 2 achieved the highest value (0.048404) compared to portfolio 1 (0.034465), indicating that portfolio 2 shows a better risk-adjusted return than portfolio 1.

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Journal Info

Abbrev

barekeng

Publisher

Subject

Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

Description

BAREKENG: Jurnal ilmu Matematika dan Terapan is one of the scientific publication media, which publish the article related to the result of research or study in the field of Pure Mathematics and Applied Mathematics. Focus and scope of BAREKENG: Jurnal ilmu Matematika dan Terapan, as follows: - Pure ...