An enhanced GRASP approach for the index tracking problem

Abstract

Index tracking models build portfolios of limited size that replicate the performance of a market index. As the size of the index grows, it becomes impractical to find an optimal solution. As far as we know, this work proposes the first greedy randomized adaptive search procedure (GRASP) approach for index tracking. GRASP has proven to be efficient in combinatorial optimization problems and offers a solution construction procedure different from the standard index tracking optimization approaches, bringing a new perspective to the field. Results showed that the proposed GRASP approach found solutions with almost the same quality as those found by CPLEX solver in a smaller time, and the proposed local search component was competitive depending on the problem parametrization. The results found have practical implications concerning the achievement of good solutions by GRASP approaches in a smaller time when compared with hybrid genetic algorithms, and new perspectives for building GRASP heuristics for portfolio optimization problems.

Model and efficient algorithm for the portfolio selection problem with real‐world constraints under value‐at‐risk measure

“…Furthermore, as pointed out by Yoshimoto (1996) and Najafi and Mushakhian (2015), transaction costs (including fixed and variable components) are one of the main concerns of today's portfolio managers, and ignoring them may result in unsatisfactory outcomes. Another main extension of the Markowitz model is the risk controlling by other measures except for the variance such as worst‐case (Chen and Korn, 2019; Korn and Leoff, 2019), Omega‐ratio (Sehgal and Mehra, 2021; Yu et al., 2023), Sharp‐ratio (Jing et al., 2022), value‐at‐risk (VaR) (Wozabal, 2012), conditional VaR (CVaR) (Sehgal and Mehra, 2019; Filippi et al., 2020), multivariate CVaR (Noyan and Rudolf, 2013), mean‐reversion (Mousavi and Shen, 2022), as well as the idea of index‐tracking (Wu et al., 2017; Hooshmand and MirHassani, 2022; Soares Silva et al., 2022).…”