Portfolio Optimization across Various Types of Variance-Covariance Matrices Using The Sequential Quadratic Programming (SQP)

Lutfi Mardianto (Institut Teknologi Sumatera)
Mira Mustika (Institut Teknologi Sumatera)
Eristia Arfi (Institut Teknologi Sumatera)
Ramanda Ditra Kristian (Institut Teknologi Sumatera)
Nayla Nurul Aisyah (Institut Teknologi Sumatera)
Prismahardi Aji Riyantoko (Okayama University)

Vygotsky: Jurnal Pendidikan Matematika dan Matematika
Vol. 8 No. 2 (2026): Vygotsky: Jurnal Pendidikan Matematika dan Matematika

This study analyzes stocks provided in LQ45 index and compares the performance of ten stocks with highest expected returns between Danantara and non-Danantara groups. The data are used to estimate parameters for optimization. The Markowitz model is employed to construct portfolios based on risk and expected return, requiring the derivation of a variance-covariance matrix. This matrix is compared with those generated by the Single Index Model (SIM) and Constant Correlation Model to evaluate differences among approaches. The nonlinear optimization problem is solved using Sequential Quadratic Programming (SQP). At an expected return of 0.2597%, all matrices allocate weights to a single stock, while setting it to zero changes portfolio proportions without altering the Sharpe ratio.