Integrating Cluster Analysis and Mean-Variance Optimization in Constructing an Optimal Sharia Stock Portfolio
Fitri Amanah

Universitas Islam Bandung

Abstract

A portfolio is a collection of investment assets designed to minimize risk through diversification across various asset classes. In the portfolio formation process, cluster analysis helps group stocks based on specific financial characteristics. This study applies Ward clustering method to group stocks based on profitability indicators, namely Return on Assets (ROA), Return on Equity (ROE), and Revenue. Furthermore, apply the Markowitz Mean-Variance model to determine the optimal asset allocation. The results show that IDX Sharia Growth stocks from December 2023 to August 2024 can be grouped into three clusters with a silhouette value of 0.5373039. Cluster I consists of stocks with high average ROA and ROE values. Cluster II contains stocks with relatively high average Revenue values, while Cluster III includes stocks with relatively low ROA, ROE, and Revenue. Next, select one representative from each cluster to form a mean-variance portfolio: ESSA, INDF, and SIDO. Portfolio optimization used various gamma values to reflect investor risk preferences. At low gamma values (e.g., gamma = 0.5), the expected return reached 0.0456, but was accompanied by a higher risk level of 0.2029. Exploring gamma values from 0 to near infinity revealed that as the gamma value increased, the portfolio expected return and risk tended to decrease in tandem.

Keywords: Ward Clustering, Mean-Variance, Portfolio, Risk

Topic: Mathematics