A comparative study of Hilbert transform and Fourier transform methods to complex-based global minimum variance portfolio - Nurwahidah; Bahri, Mawardi; Rahim, Amran (Statistics, Optimization & Information Computing, 2025)
Quantitative method in portfolio construction is an engaging issue in mathematical finance. A number of studies have shown the role of real numbers in constructing portfolio. However, very little attention has been paid to the role of complex number in finance. The principal objective of this project is to construct complex-based Global Minimum Variance (GMV) portfolio and apply clustering method in asset selection. The findings indicate that the GMV with Hilbert transform method has lower standard deviation in general than the real-based GMV portfolio. On the other hand, GMV portfolio approached by Fourier Transform shows higher standard deviation than complex-based portfolio with Hilbert transform and real-based portfolio. Our findings show how to develop GMV portfolio with Hilbert and Fourier Transform approach for constructing complex-based optimal portfolio.