Clustering Jakarta Islamic Index Stocks Using Fuzzy C-Means Clustering  and Determining Optimal Portfolio Using Capital Asset Pricing Model

Zidni Ilma Nafi'a; Agung Prabowo; Agus Sugandha; Diah Paramita Amitarwati

Zidni Ilma Nafi'a Mathematics Study Program, Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Jenderal Soedirman, Purwokerto, Indonesia.
Agung Prabowo Statistics Study Program, Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Jenderal Soedirman, Purwokerto, Indonesia.
Agus Sugandha Mathematics Study Program, Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Jenderal Soedirman, Purwokerto, Indonesia.
Diah Paramita Amitarwati Sharia Economics Study Program, Faculty of Islamic Economics and Business, Universitas Islam Negeri Prof. K.H. Saifuddin Zuhri, Purwokerto, Indonesia.

Abstract

Investment is an activity of investing fund or capital to earn profits in the future. One investment instrument that many people prefer is stocks, especially those included in stock market index, such as Jakarta Islamic Index (JII). To maximize returns and minimize risks, portfolio is formed. Stock clustering by their financial performance can be done using the so-called Fuzzy C Means Clustering, a method to cluster data based on membership degrees. This research aims at clustering the stocks included in JII using the Fuzzy C-Means Clustering algorithm. Four financial ratios, namely Return on Assets, Current Ratio, Debt to Equity Ratio, and Total Asset Turnover, were employed to do this. The resulting clustering was then used to form an optimal portfolio using a method known as Capital Asset Pricing Model (CAPM). This model aimed to calculate the expected returns and risks of each portfolio. Two methods were used in this research, they were literature review and a case study in the stocks included in JII. Based on the Silhouette coefficient value, this research generated three optimal clusters of stocks included in JII. The portfolio made using CAPM method produced INKP and UNVR stocks in cluster 1, at an investment weight of 5% and 95% respectively. In cluster 2, the stocks of ACES, ADMR, EMTK, ICBP, ITMG, and MIKA formed a portfolio with investment weights of 1%, 1%, 1%, 1%, 1%, and 95% respectively. In cluster 3, the stocks of ADRO, AKRA, ANTM, ASII, BRIS, BRMS, CPIN, EXCL, INDF, INTP, PGAS, SMGR, and UNTR, formed a portfolio with investment weights of 6.66%, 2.01%, 4.95%, 20.86%, 7.65%, 10.68%, 6.69%, 5.64%, 21.08%, 3.14%, 1.91%, 3.98%, and 4.75% respectively. The portfolio performance was evaluated using Sharpe ratio and it led to negative results, i.e., 0.2501 for cluster 1, -0.0405 for cluster 2, and -0.0587 for cluster 3. It is, therefore, recommended that investors invest more in the cluster 2 portfolio or choose risk-free assets instead.