Optimasi Portofolio Saham Menggunakan Mean-Variance dengan Penyelesaian Quadratic Programming

Abstract

Optimasi portofolio saham menjadi hal penting bagi investor dalam menyeimbangkan antara return dan risiko. Penelitian ini bertujuan mengoptimalkan portofolio saham di Indonesia menggunakan metode mean-variance dengan penyelesaian quadratic programming. Data yang digunakan berupa harga saham mingguan 697 emiten di Bursa Efek Indonesia periode 1 Januari 2021-1 Januari 2023. Saham dikelompokkan menggunakan k-means clustering berdasarkan return dan risiko, menghasilkan tiga cluster dengan karakteristik risiko-return berbeda. Cluster 3 dipilih sebagai yang paling efisien dengan Sharpe ratio tertinggi 4,8794. Optimasi portofolio dilakukan menggunakan fungsi solve.QP() di RStudio dengan variasi nilai toleransi risiko investor dalam rentang 0,1 sampai 1. Hasil menunjukkan toleransi risiko pada nilai 0,1 memberikan Sharpe ratio tertinggi 7,8171, menandakan portofolio paling efisien. Peningkatan nilai toleransi risiko meningkatkan return dan risiko secara bersamaan namun menurunkan efisiensi. Metode ini berhasil menggambarkan hubungan positif antara expected return dan risiko melalui kurva efficient frontier.

Stock portfolio optimization is essential for investors to balance return and risk. This study aims to optimize stock portfolios in Indonesia using the mean-variance method with a quadratic programming approach. The data used consist of weekly stock prices from 697 listed companies on the Indonesia Stock Exchange for the period January 1, 2021–January 1, 2023. Stocks were grouped using k-means clustering based on return and volatility, resulting in three clusters with different risk–return characteristics. Cluster 3 was identified as the most efficient, with the highest Sharpe ratio of 4,8794. Portfolio optimization was conducted using the solve.QP() function in RStudio with variations in investor risk tolerance values ranging from 0,1 to 1. The results show risk tolerance with a value of 0,1 provides the highest Sharpe ratio of 7,8171, indicating the most efficient portfolio. Increasing the risk tolerance value raises both return and risk but decreases efficiency. Overall, this method successfully illustrates the positive relationship between expected return and risk through the efficient frontier curve.