Electronic Theses and Dissertation

Investasi saham memiliki potensi keuntungan yang tinggi, namun juga diiringi dengan risiko yang besar, sehingga diperlukan metode optimisasi portofolio yang mampu menyeimbangkan antara return dan risiko. Penelitian ini bertujuan untuk membentuk portofolio saham optimal menggunakan metode Nadir Compromise Programming (NCP) dengan pendekatan Expected Shortfall (ES) sebagai ukuran risiko ekstrem. Studi kasus dilakukan pada saham-saham yang tergabung dalam indeks NASDAQ-100. Data yang digunakan berupa harga penutupan harian 20 saham selama periode 20 Mei 2024 hingga 20 Mei 2025. Berdasarkan uji normalitas Kolmogorov–Smirnov, diperoleh enam saham yang berdistribusi normal, yaitu MELI, NFLX, NVDA, ORLY, TSLA, dan ZS, yang digunakan dalam pembentukan portofolio. Model NCP dibangun dengan tiga fungsi tujuan, yaitu mengoptimalkan koefisien risiko beta, memaksimalkan expected return, dan meminimalkan biaya investasi, serta diselesaikan menggunakan perangkat lunak LINGO dengan beberapa skenario batas proporsi dana dari 20% sampai 100% dengan kenaikan 10% setiap skenario. Hasil penelitian menghasilkan sembilan portofolio optimal. Evaluasi risiko dilakukan menggunakan Expected Shortfall dan kinerja portofolio diukur dengan Stable Tail Adjusted Return Ratio (STARR). Portofolio dengan batas atas proporsi dana 20% memiliki nilai STARR tertinggi sebesar 0,04920, sehingga dinyatakan sebagai portofolio optimal terbaik.

Kata kunci: Portofolio Saham, Nadir Compromise Programming, Expected Shortfall

Stock investment offers high potential returns but is also accompanied by significant risk, therefore, a portfolio optimization method that balances return and risk is required. This study aims to construct an optimal stock portfolio using the Nadir Compromise Programming (NCP) method with the Expected Shortfall (ES) approach as a measure of extreme risk. The case study is conducted on stocks included in the NASDAQ-100 index. The data used consist of daily closing prices of 20 stocks over the period from May 20, 2024, to May 20, 2025. Based on the Kolmogorov–Smirnov normality test, six stocks with normally distributed returns were obtained, namely MELI, NFLX, NVDA, ORLY, TSLA, and ZS, which were used in portfolio construction. The NCP model is formulated with three objective functions, optimizing the beta risk coefficient, maximizing expected return, and minimizing investment cost, and is solved using LINGO software under several upper-bound allocation scenarios ranging from 20% to 100% with a 10% increment for each scenario. The results yield nine optimal portfolios. Risk evaluation is conducted using Expected Shortfall, and portfolio performance is measured using the Stable Tail Adjusted Return Ratio (STARR). The portfolio with a 20% upper-bound allocation achieves the highest STARR value of 0.04920 and is therefore identified as the best optimal portfolio. Keywords: Stock Portfolio, Nadir Compromise Programming, Expected Shortfall.