Sains Malaysiana 54(2)(2025): 601-609

http://doi.org/10.17576/jsm-2025-5402-24

 L0 Norm Sparse Portfolio Optimisation using Proximal Spectral Gradient Method on Malaysian Stock Market

 (Pengoptimuman Portfolio Jarang L0 Norma menggunakan Kaedah Kecerunan Spektrum Proksimal dalam Pasaran Saham Malaysia)

KEVIN CHOON LIANG YEW¹, WAI KUAN WONG^1,*, HONG SENG SIM¹, YONG KHENG GOH¹, WEI YEING PAN¹, SHIN ZHU SIM²

Diserahkan: 2 Januari 2024/Diterima: 22 November 2024

¹Centre for Mathematical Sciences, Universiti Tunku Abdul Rahman, Bandar Sungai Long, 43000 Kajang, Selangor, Malaysia

²School of Mathematical Sciences, University of Nottingham Malaysia, Jalan Broga, 43500 Semenyih, Selangor, Malaysia

ABSTRACT

In this paper, we introduce a modified norm-constraint mean-variance portfolio selection method. First, we use the Augmented Lagrangian method (ALM) to convert the objective function to an unconstrained objective function. Then we apply the proximal spectral gradient method (PSG) onto the unconstrained objective function to find an optimal sparse portfolio. This novel sparse portfolio optimization procedure encourages sparsity in the entire portfolio using norm. The PSG utilizes a multiple damping gradient (MDG) method to solve the smooth terms of the function. The step size is computed using the Lipschitz constant. Also, PSG uses the iterative thresholding method (ITH) to solve norm and induce the sparsity of the portfolio. The performance of the PSG is illustrated by its application on the Malaysian stock market. It is found that PSG’s sparse portfolio outperforms the equal weightage portfolio when the initial portfolio size is around 100 stocks and is prefiltered using the Sharpe ratio or the coefficient of variation.

Keywords:  norm, sparse portfolio optimization, proximal spectral gradient, Malaysia stock market

ABSTRAK

Dalam kertas kerja ini, kami memperkenalkan kaedah pemilihan portfolio min-varians kekangan norma yang diubahsuai. Pada awalnya, kami menggunakan Kaedah Augmented Lagrangian (ALM) untuk mengubah fungsi objektif kepada fungsi objektif tanpa sekatan. Seterusnya, kami memakai kaedah kecerunan proksimal spektrum (PSG) ke atas fungsi objektif tanpa sekatan tersebut untuk mendapat portfolio jarang optimum. Prosedurpengoptimuman portfolio jarang yang novel ini menggalakkan jarang bagi portfolio keseluruhan dengan menggunakan norma. PSG menggunakan kaedah kecerunan redaman berbilang (MDG) untuk menyelesaikan sebutan-sebutan licin pada fungsi tersebut. Saiz langkah dikira dengan menggunakan pemalar Lipschitz. Tambahan pula, PSG menggunakan kaedah ambang berbilang (ITH) untuk menyelesaikan norma dan menggalakkan jarang bagi portfolio. Prestasi PSG ini digambarkan dengan aplikasinya ke atas pasaran saham Malaysia. Didapati bahawa portfolio jarang yang dicadangkan mendahalui prestasi portfolio berwajaran sama apabila saiz portfolio permulaan adalah kira-kira 100 saham dan telah ditapis dengan nisbah Sharpe atau pekali variasi.

Kata kunci:  norma, pengoptimuman portfolio jarang, kecerunan proksimal spektrum, pasaran saham Malaysia

RUJUKAN

Cauchy, A. 1847. Méthode générale pour la résolution des systemes d’équations simultanées. Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences. 25: 536–538.

Chen, J., Dai, G., & Zhang, N. 2020. An application of sparse-group LASSO regularization to equity portfolio optimization and sector selection. Annals of Operations Research 284(1): 243–262.

Chopra, V. K., & Ziemba, W. T. 1993. The effect of errors in means, variances, and covariances on optimal portfolio choice. The Journal of Portfolio Management 19(2): 6–11.

DeMiguel, V., Garlappi, L., & Uppal, R. 2011. “Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy?” In Gerd Gigerenzer, Ralph Hertwig, and Thorsten Pachur (eds), Heuristics: The Foundations of Adaptive Behavior: 644–667.

Gotoh, J., & Takeda, A. 2011. On the role of norm constraints in portfolio selection. Computational Management Science 8(4): 323–353

Hawkins, D. M., & Weisberg, S. 2017. Combining the Box-Cox power and generalised log transformations to accommodate nonpositive responses in linear and mixed-effects linear models. South African Statistical Journal 51(2): 317–328.

Hwang, I., Xu, S., & In, F. 2018. Naive versus optimal diversification: Tail risk and performance. European Journal of Operational Research 265(1): 372–388.

Jagannathan, R., & Ma, T. 2003. Risk reduction in large portfolios: Why imposing the wrong constraints helps. The Journal of Finance 58(4): 1651–1683.

Kremer, P. J., Lee, S., Bogdan, M., & Paterlini, S. 2020. Sparse portfolio selection via the sorted - norm. Journal of Banking & Finance 110: 105687.

Luenberger, D. G. & Ye, Y. 2021. Linear and nonlinear programming. 5th ed. Cham Switzerland: Springer.

Manly, B. F. J. 1976. Exponential Data Transformations. Journal of the Royal Statistical Society Series D: The Statistician 25(1): 37–42

Markowitz, H. 1952. Portfolio selection. The Journal of Finance 7(1): 77–91.

Olivares-Nadal, A. V., & DeMiguel, V. 2018. Technical note—A robust perspective on transaction costs in portfolio optimization. Operations Research 66(3): 733–739.

Sim, H. S., Leong, W. J., & Chen, C. Y. 2019. Gradient method with multiple damping for large-scale unconstrained optimization. Optimization Letters 13(3): 617–632.

Sim, H. S., Ling, W. S. Y., Leong, W. J., & Chen, C. Y. 2023. Proximal linearized method for sparse equity portfolio optimization with minimum transaction cost. Journal of Inequalities and Applications 152(2023).

Wang, H., Zhang, W., He, Y., & Cao, W. 2023. - norm based short-term sparse portfolio optimization algorithm based on alternating direction method of multipliers. Signal Processing 208(2023): 108957

Woo, G. Y. H., Sim, H. S., Goh, Y. K., & Leong, W. J. 2023. Proximal variable metric method with spectral diagonal update for large scale sparse optimization. Journal of the Franklin Institute 360(7): 4640–4660

*Pengarang untuk surat-menyurat; email: wongwk@utar.edu.my