Pembentukan Portofolio Robust Mean-Variance Saham Syariah Jakarta Islamic Index (JII) Melalui Pendekatan Analisis Klaster K-Medoids
DOI:
https://doi.org/10.29313/statistika.v24i2.3994Keywords:
Estimasi Robust, K-Medoids, Mean-Variance, PortofolioAbstract
ABSTRAK
Portofolio adalah kumpulan dari beberapa aset. Tujuan pembentukan portofolio yaitu untuk menghasilkan return yang paling tinggi sambil mengurangi risiko. Untuk menghindari outlier yang sering terjadi dalam portofolio model Mean-Variance (MV), perlu menggunakan estimasi robust. Data penelitian menggunakan closing price bulanan dari saham-saham yang konsisten selalu masuk ke dalam kelompok Jakarta Islamic Index (JII) periode Januari 2019 – Juni 2023. Tahap awal analisis menggunakan teknik klastering metode K-Medoids berdasarkan pada nilai expected return dan risiko. Klasterisasi dilakukan untuk menghemat waktu dan menekan biaya manajemen portofolio. Hasil analisis klaster menciptakan dua klaster. Saham INCO dan ADRO mewakili klaster pertama, dan saham KLBF dan AKRA mewakili klaster kedua. Keempat saham representasi tersebut dibentuk portofolio MV robust S dan portofolio MV robust Constrained-M (CM). Kinerja portofolio diukur menggunakan sharpe ratio. Hasil analisis menunjukkan bahwa kinerja model portofolio robust MV estimasi Constrained-M (CM) mengungguli kinerja model portofolio robust MV estimasi S.
ABSTRACT
A portfolio is an assortment of several items. The goal of portfolio construction is to get the maximum return at the least amount of risk. Robust estimate is a means to mitigate the sensitivity of the Mean-Variance (MV) model portfolio to outliers. The research data uses monthly closing prices of stocks that are consistently included in the Jakarta Islamic Index (JII) group for the period January 2019 - June 2023. The initial stage of analysis uses the K-Medoids method clustering technique based on the expected return and risk values. The purpose of the clustering is for time efficiency and to reduce the amount of costs in managing the portfolio. The results of the cluster analysis formed two clusters, where the first cluster is represented by INCO and ADRO stocks. While the second cluster is represented by KLBF dan AKRA stocks. The four representative stocks are formed MV robust S portfolio and MV robust Constrained-M (CM) portfolio. Portfolio performance is measured using the sharpe ratio. According to the analysis's findings, the Constrained-M (CM) estimation MV robust portfolio model performs better than the S estimation MV robust portfolio model.
References
Adyana, I. M. (2020). Manajemen Investasi dan Portofolio. Lembaga penerbitan Universitas Nasional.
Azim, M. F., Azizah, A., & Anggraini, D. (2021). Optimasi Bobot Portofolio Menggunakan Algoritma Genetika. Jurnal Sains Matematika Dan Statistika, 7(1), 58. https://doi.org/10.24014/jsms.v7i1.12190
Davies, P. L. (1987). Asymptotic Behaviour of S-Estimates of Multivariate Location Parameters and Dispersion Matrices. JSTOR, Vol. 15, 1269–1292. http://www.jstor.com/stable/2241828
DeMiguel, V., & Nogales, F. (2009). Portfolio Selection With Robust Estimation. Operations Research, 57(3), 560–577.
Gubu, L., Rosadi, D., & Abdurakhman. (2020). Robust Mean-Variance Portfolio Selection With Ward And Complete Linkage Clustering Algorithm. Economic Computation and Economic Cybernetics Studies and Research, 54(3), 111–127. https://doi.org/10.24818/18423264/54.3.20.07
Gubu, L., Rosadi, D., & Abdurakhman, A. (2021). Pembentukan Portofolio Saham Menggunakan Klastering Time Series K-Medoid dengan Ukuran Jarak Dynamic Time Warping. Jurnal Aplikasi Statistika & Komputasi Statistik, 13(2), 35–46. https://doi.org/10.34123/jurnalasks.v13i2.295
Hardin, J. S. (2000). Multivariate Outlier Detection and Robust Clustering with Minimum Covariance Determinant Estimation and -Estimation. University of California.
Kaufman, L., & Raousseeuw, P. (1990). Finding Groups in Data: An Introduction to Cluster Analysis. John Wiley and Son, Inc.
Kent, J. ., & Tyler, D. . (1996). Constrained M-Estimation for Multivariate Location and Scatter. Journal Annals of Statistic, 24(3).
Markowitz, H. (1952). Portofolio Selection. The Journal of Finance, 7(1), 77–91.
Supandi, E. D. (2017). Pengembangan Model Portofolio Mean-Variance Melalui Metode Estimasi Robust dan Optimasi Robust.
Supandi, E. D., & Anggara, Y. (2023). Analisis Klaster dalam Pembentukan Portofolio Robust Mean-Variance. Jurnal Sains Matematika Dan Statistika, 9(1), 37–47.
Vercillis, C. (2009). Business Intelligance: Data Mining and Optimization for Decision Making. WILEY.
Winston, W. L., & Goldberg, J. B. (2004). Operations Research: Applications and Algorithms, Thomson Learning Inc. (Fourth Edi).
