CONSTRUCTING AN OPTIMAL PORTFOLIO USING CLUSTERING LARGE APPLICATION AND VALUE AT RISK ANALYSIS FOR IDX80 STOCKS
Abstract
Investment is a way to manage wealth and achieve financial goals in the future. Stocks are an attractive investment instrument due to their high potential returns, although they also carry significant risks. These risks can be minimized through portfolio diversification. Diversification is carried out by selecting representative stocks from the clustering results. This study aims to construct an optimal portfolio using the Clustering Large Application (CLARA) method and conduct portfolio risk analysis using Value at Risk (VaR). The data used includes IDX80 stock closing prices from November 1, 2024, to January 31, 2025, the financial ratios of IDX80 stocks on December 2024, and the Bank Indonesia (BI-Rate) interest rate from November 2024 to January 2025. The CLARA method produces four stock clusters with a silhouette coefficient of 0.18226. This value indicates a low level of separation between clusters, as there might be overlapping features among the clusters. Representative stocks from each cluster are selected based on the highest Sharpe ratio: SCMA, JPFA, GOTO, and BRIS. The portfolio weights based on MVEP are 15.002% (SCMA), 29.786% (JPFA), 1.858% (GOTO), and 53.354% (BRIS). The VaR calculation shows a potential maximum loss of Rp137,139 in one day, with a 99% confidence level, from an initial investment of Rp10,000,000.
Downloads
References
Z. Bodie, A. Kane, and A. J. Marcus, INVESTMENTS, 11th ed. New York: McGraw Hill Education, 2017.
Z. Bodie, R. C. Merton, and R. T. Thakor, PRINCIPLES OF FINANCE. Cambridge: Cambridge University Press, 2025. doi: https://doi.org/10.1017/9781108982610.
N. Jha, R. S. Mishra, and S. M. Bhome, INVESTMENT ANALYSIS AND PORTFOLIO MANAGEMENT. Mumbai: Himalaya Publishing House, 2016. [Online]. Available: www.himpub.com
L. Gubu, D. Rosadi, and Abdurakhman, “PEMBENTUKAN PORTOFOLIO SAHAM MENGGUNAKAN KLASTERING TIME SERIES K-MEDOID DENGAN UKURAN JARAK DYNAMIC TIME WARPING,” J. Apl. Stat. Komputasi Stat., vol. 13, no. 2, pp. 35–46, 2021, doi: https://doi.org/10.34123/jurnalasks.v13i2.295.
S. J. Sinaga, N. Satyahadewi, and H. Perdana, “DETERMINING THE OPTIMUM NUMBER OF CLUSTERS IN HIERARCHICAL CLUSTERING USING PSEUDO-F,” Euler J. Ilm. Mat. Sains dan Teknol., vol. 11, no. 2, pp. 372–382, Dec. 2023, doi: https://doi.org/10.37905/euler.v11i2.23113.
C. C. Aggarwal, OUTLIER ANALYSIS. Springer International Publishing, 2017. doi: https://doi.org/10.1007/978-3-319-47578-3.
P.-N. Tan, M. Steinbach, A. Karpatne, and V. Kumar, INTRODUCTION TO DATA MINING, 2nd ed. New York: Pearson Education, 2019.
R. Lapiza, Syafriandi, N. Amalita, and D. Fitria, “GROUPING THE DISTRICTS IN SUMATERA REGION BASED ON ECONOMIC DEVELOPMENT INDICATORS USING K-MEDOIDS AND CLARA METHODS,” UNP J. Stat. Data Sci., vol. 1, no. 1, pp. 16–22, Feb. 2023, doi: https://doi.org/10.24036/ujsds/vol1-iss1/13.
A. P. Ayuni, D. Kusnandar, and S. Martha, “IMPLEMENTASI ALGORITMA K-MEDOIDS DAN CLUSTERING LARGE APPLICATIONS (CLARA) DENGAN OPTIMASI SILHOETTE COEFFICIENT (STUDI KASUS: PENGELOMPOKAN INDEKS PEMBANGUNAN MANUSIA BERDASARKAN KABUPATEN/KOTA DI INDONESIA),” Bul. Ilm. Math. Stat. dan Ter., vol. 13, no. 2, pp. 191–200, 2024, doi: https://doi.org/10.26418/bbimst.v13i2.76959.
A. N. Pratama, N. Satyahadewi, and E. Sulistianingsih, “ANALYSIS OF OPTIMAL PORTFOLIO FORMATION ON IDX30 INDEXED STOCK WITH THE MEAN ABSOLUTE DEVIATION METHOD,” BAREKENG J. Ilmu Mat. dan Terap., vol. 18, no. 3, pp. 1753–1764, Jul. 2024, doi: https://doi.org/10.30598/barekengvol18iss3pp1753-1764.
A. Silvia and M. Rosha, “ANALISIS PERBANDINGAN PORTOFOLIO OPTIMAL MODEL MARKOWITZ DAN MODEL MVEP (STUDI KASUS SAHAM LQ-45 DI BURSA EFEK INDONESIA DI MASA PANDEMI COVID-19),” J. Math. UNP, vol. 9, no. 2, pp. 125–131, 2024.
D. R. Prihatiningsih, D. A. I. Maruddani, and R. Rahmawati, “VALUE AT RISK (VAR) DAN CONDITIONAL VALUE AT RISK (CVAR) DALAM PEMBENTUKAN PORTOFOLIO BIVARIAT MENGGUNAKAN COPULA GUMBEL,” J. Gaussian, vol. 9, no. 3, pp. 326–335, 2020, doi: https://doi.org/10.14710/j.gauss.v9i3.28913.
S. Margun, N. Satyahadewi, and H. Perdana, “ANALISIS KINERJA PORTOFOLIO OPTIMAL SAHAM LQ-45 DENGAN METODE MEAN-GIINI MENGGUNAKAN INDEKS SHARPE,” Bul. Ilm. Mat. Stat. dan Ter., vol. 11, no. 3, pp. 423–430, 2022, doi: 10.26418/bbimst.v11i3.54959.
M. N. Siddikee, “EFFECT OF DAILY DIVIDEND ON ARITHMETIC AND LOGARITHMIC RETURN,” J. Financ. Data Sci., vol. 4, no. 4, pp. 247–272, Dec. 2018, doi: https://doi.org/10.1016/j.jfds.2018.06.001
M. Azis, S. Mintarti, and M. Nadir, MANAJEMEN INVESTASI, FUNDAMENTAL, TEKNIKAL, PERILAKU INVESTOR, DAN RETURN SAHAM. Yogyakarta: Deepublish, 2015.
D. Schoenmaker and W. Schramade, CORPORATE FINANCE FOR LONG-TERM VALUE. Cham: Springer, 2023. doi: https://doi.org/10.1007/978-3-031-35009-2
T. Latunde, L. S. Akinola, and D. D. Dare, “ANALYSIS OF CAPITAL ASSET PRICING MODEL ON DEUTSCHE BANK ENERGY COMMODITY,” Green Financ., vol. 2, no. 1, pp. 20–34, 2020, doi: https://doi.org/10.3934/GF.2020002.
N. Shrestha, “DETECTING MULTICOLLINEARITY IN REGRESSION ANALYSIS,” Am. J. Appl. Math. Stat., vol. 8, no. 2, pp. 39–42, Jun. 2020, doi: https://doi.org/10.12691/ajams-8-2-1.
K. Wada, “OUTLIERS IN OFFICIAL STATISTICS,” Japanese J. Stat. Data Sci., vol. 3, no. 2, pp. 669–691, Dec. 2020, doi: https://doi.org/10.1007/s42081-020-00091-y.
P. R. Fitrayana and D. R. S. Saputro, “ALGORITME CLUSTERING LARGE APPLICATION (CLARA) UNTUK MENANGANI DATA OUTLIER,” Prism. Pros. Semin. Nas. Mat., vol. 5, pp. 721–725, 2022, [Online]. Available: https://journal.unnes.ac.id/sju/index.php/prisma
D. Sawitri, “PERAN DEEP LEARNING DAN BIG DATA DALAM MENDETEKSI MASALAH KEUANGAN,” J. Teknol. Inf., vol. 6, no. 1, pp. 193–207, 2025, doi: https://doi.org/10.46576/djtechno.v6i1.6037.
J. Rathee, P. Kaur, and A. Singh, “FUZZY CLUSTERING BASED NOISY IMAGE SEGMENTATION OF MRI/CT SCAN BRAIN TUMOR IMAGES USING DIFFERENT DISTANCE METRICS AS SIMILARITY MEASURE,” SN Comput. Sci., vol. 5, no. 777, Aug. 2024, doi: https://doi.org/10.1007/s42979-024-03102-x.
M. Z. Rodriguez et al., “CLUSTERING ALGORITHMS: A COMPARATIVE APPROACH,” PLoS One, vol. 14, no. 1, pp. 1–34, Jan. 2019, doi: https://doi.org/10.1371/journal.pone.0210236.
V. P. Senthilnathan, M. Singaravelu, S. Rajendran, and S. Srinivas, “A CLUSTERING-METAHEURISTIC-SIMULATION APPROACH TO DETERMINE AIR TAXI OPERATING SITE LOCATION,” Transp. Res. Interdiscip. Perspect., vol. 29, Jan. 2025, doi: https://doi.org/10.1016/j.trip.2025.101330.
E. Schubert and P. J. Rousseeuw, “FAST AND EAGER K-MEDOIDS CLUSTERING: O(K) RUNTIME IMPROVEMENT OF THE PAM, CLARA, AND CLARANS ALGORITHMS,” Inf. Syst., vol. 101, Nov. 2021, doi: https://doi.org/10.1016/j.is.2021.101804.
A. Et-Taleby, M. Boussetta, and M. Benslimane, “FAULTS DETECTION FOR PHOTOVOLTAIC FIELD BASED ON K-MEANS, ELBOW, AND AVERAGE SILHOUETTE TECHNIQUES THROUGH THE SEGMENTATION OF A THERMAL IMAGE,” Int. J. Photoenergy, vol. 2020, 2020, doi: https://doi.org/10.1155/2020/6617597
D. A. I. C. Dewi and D. A. K. Pramita, “ANALISIS PERBANDINGAN METODE ELBOW DAN SILLHOUETTE PADA ALGORITMA CLUSTERING K-MEDOIDS DALAM PENGELOMPOKAN PRODUKSI KERAJINAN BALI,” J. MATRIX, vol. 9, no. 3, pp. 102–109, 2019, doi: https://doi.org/10.31940/matrix.v9i3.1662.
J. Raymaekers and P. J. Rousseeuw, “SILHOUETTES AND QUASI RESIDUAL PLOTS FOR NEURAL NETS AND TREE-BASED CLASSIFIERS,” J. Comput. Graph. Stat., vol. 31, no. 4, pp. 1332–1343, 2022, doi: https://doi.org/10.1080/10618600.2022.2050249.
A. H. Manurung, A. Manurung, N. M. Machdar, and J. Sijabat, “STOCK SELECTION USING SEMI-VARIANCE AND BETA TO CONSTRUCT PORTFOLIO AND EFFECT MACRO-VARIABLE ON PORTFOLIO RETURN,” Turkish J. Comput. Math. Educ., vol. 15, no. 1, pp. 14–25, 2024, doi: https://doi.org/10.61841/turcomat.v15i1.14350.
K. Hanum, Tarno, and Sudarno, “OPTIMASI VALUE AT RISK REKSA DANA MENGGUNAKAN METODE ROBUST EXPONENTIALLY WEIGHTED MOVING AVERAGE (ROBUST EWMA) DENGAN PROSEDUR VOLATILITY UPDATING HULL AND WEHITE,” J. GAUSSIAN, vol. 6, no. 3, pp. 375–384, 2017, doi: 10.14710/j.gauss.6.3.375-384.
A. B. Schmidt, “MANAGING PORTFOLIO DIVERSITY WITHIN THE MEAN VARIANCE THEORY,” Ann. Oper. Res., vol. 282, pp. 315–329, Nov. 2019, doi: https://doi.org/10.1007/s10479-018-2896-x.
I. E. Etuk, Y. Musa, and U. Gulumbe, “Estimating and Predicting Value at Risk in Selected Banks of Nigeria Stock Market,” Int. J. Stat. Appl., vol. 9, no. 4, pp. 117–121, 2019, doi: 10.5923/j.statistics.20190904.03.
A. Solihatun, L. Gubu, Aswani, E. Cahyono, and L. O. Saidi, “PERHITUNGAN VALUE AT RISK (VAR) PADA PORTOFOLIO SAHAM IDX SEKTOR KEUANGAN (IDXFINANCE) MENGGUNAKAN METODE SIMULASI HISTORIS (HISTORICAL SIMULATION METHOD),” J. Mat. Komputasi dan Stat., vol. 3, no. 1, pp. 245–254, 2023, doi: https://doi.org/10.33772/jmks.v3i1.32
Copyright (c) 2026 Sania Pujianti, Hendra Perdana, Neva Satyahadewi
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this Journal agree to the following terms:
- Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
- Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
- Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.
1.gif)
