Portfolio Optimization for Rupiah Exchange Rate using Multidimensional Geometric Brownian Motion Model - Masitah, Siti; Budiarti, Retno; Purnaba, I Gusti Putu (JTAM (Jurnal Teori dan Aplikasi Matematika), 2025)
Exchange rate fluctuations are critical in ensuring economic stability and shaping foreign investment, while foreign currencies serve as asset and wealth diversification instruments. This study aims to predict foreign exchange rates with a multidimensional geometric Brownian motion model and determine the optimal portfolio fund allocation with the Markowitz model using the Moore-Pendrose method. The multidimensional GBM model was employed for its ability to capture the volatility and interdependence among multiple currencies, making it more suitable for multi-asset portfolios than univariate models. The Markowitz model was used to determine the optimal asset allocation that achieves a specified expected return with minimal risk, while the Moore-Penrose method was applied to address matrix inversion challenges in high-dimensional data. Using data from 2023 to April 2024 on the Indonesian rupiah against the Singapore Dollar (SGD), Chinese Yuan (CNY), and Euro (EUR), this study finds that the multidimensional GBM model effectively forecasts exchange rate movements, as indicated by MAPE values below 10% for each currency. "The optimal portfolio yields a risk of 0.28% and an expected return of 0.009%, with asset allocations of 90.3% in SGD, 8.2% in CNY, and 1.5% in EUR. The dominance of SGD in the optimal portfolio suggests it was the most favorable investment option against the rupiah during the study period. This reflects Singapore's strong economic fundamentals and strategic position as a global financial hub. These findings provide valuable insights for investors and financial analysts seeking to manage currency risk and enhance returns through data-driven diversification strategies.