Optimasi Portofolio Saham IDX30 Menggunakan Copula t-Student Berbasis Omega Ratio

Abstract

Pasar saham modern cenderung menunjukkan distribusi return yang asimetris, ber-ekor tebal, serta dependence nonlinier antar aset, sehingga pendekatan optimasi portofolio berbasis mean-variance menjadi kurang memadai dalam merepresentasikan risiko aktual. Penelitian ini bertujuan untuk mengoptimalkan portofolio saham IDX30 dengan mengintegrasikan omega ratio sebagai fungsi objektif dan pemodelan dependence non linier berbasis copula t-Student. Data yang digunakan berupa harga penutupan harian saham-saham IDX30 periode 2019–2024. Volatilitas return masing-masing saham dimodelkan menggunakan GARCH(1,1) dengan distribusi residual standar t-Student untuk menangkap karakteristik ekor tebal dan volatility clustering. Selanjutnya, struktur dependence antar saham dimodelkan menggunakan regular vine copula (R-vine). Berdasarkan model tersebut, dilakukan simulasi Monte Carlo untuk menghasilkan distribusi return multivariat sebagai dasar optimasi portofolio. Permasalahan maksimasi omega ratio direformulasi ke dalam bentuk linear programming menggunakan transformasi Charnes–Cooper sehingga solusi optimal global dapat diperoleh secara efisien. Kinerja portofolio hasil optimasi dibandingkan dengan portofolio berbobot sama dan portofolio berbasis Omega historis. Hasil empiris menunjukkan bahwa portofolio berbasis Copula-Omega memberikan kinerja dan kekayaan akhir yang lebih tinggi serta lebih tangguh terhadap risiko ekstrem.

Modern financial markets tend to exhibit asymmetric, heavy-tailed return distributions and nonlinear dependence across assets, rendering the traditional mean–variance portfolio optimization framework inadequate for capturing actual risk. This study aims to optimize an IDX30 stock portfolio by integrating the omega ratio as the objective function and nonlinear dependence modelling based on the t-Student copula. The data consist of daily closing prices of IDX30 constituent stocks from 2019 to 2024. The volatility of individual stock returns is modelled using a GARCH(1,1) process with t-Student distributed innovations to capture fat tails and volatility clustering. The dependence structure among stocks is then modelled using a regular vine copula (R-vine). Based on the estimated GARCH–copula model, Monte Carlo simulations are conducted to generate multivariate return distributions for portfolio optimization. The omega ratio maximization problem is reformulated into a linear programming framework using the Charnes–Cooper transformation, ensuring an efficient global optimal solution. The performance of the optimized portfolio is compared with an equally weighted portfolio and a historical omega-based portfolio. Empirical results indicate that the Copula-Omega portfolio achieves superior performance, higher final wealth, and greater robustness against extreme market risk.