An index tracking model with stratified sampling and optimal allocation

Abstract

This paper investigates the portfolio strategy problem for passive fund management. We propose a novel portfolio strategy that combines the existing stratified strategy and optimized sampling strategy. The proposed method enables one to include adequate practical information in portfolio decision making, and promotes better out-of-sample performance. A mixed-integer program model is built that captures the stratification information, the cardinality requirement, and other practical constraints. The corresponding model is able to forecast and generate optimal tracking portfolios with high performance, especially in out-of-sample time period. As mixed-integer program is a well-known NP-hard problem, to tackle the computational challenge, we propose a stratified hybrid genetic algorithm, in which a novel crossover operator is introduced. To evaluate the proposed strategy and algorithm, we conduct numerical tests on real data sets collected from China Stock Exchange Markets. The experimental resultsshow that the algorithm runs efficiently and the portfolio strategy performs significantly better than other existing strategies.KEYWORDS index tracking, out-of-sample performance, stratified sampling, stratified hybrid genetic algorithm, s-rar crossover

An enhanced GRASP approach for the index tracking problem

“…The hybrid GAs of Ruiz-Torrubiano and Suarez (2009) (GA_ruiz-torrubiano2009) and Sant'Anna et al (2017b) (GA_santanna2017) were selected because they use a general-purpose solver to adjust weights, which is the same for the GRASP that was adopted in this work. Also, these two GAs have been adopted to solve different types of index tracking models (Ruiz-Torrubiano and Suarez, 2009;Wang et al, 2012;Xu et al, 2016;Sant'Anna et al, 2017b;Wang et al, 2018;de Amorim et al, 2021). Thus, this final comparison can give insights on the usability of the adapted GRASP approaches on this problem.…”

“…In an active strategy, the fund manager tries to outperform the market by picking the stocks that he/she judges to be promising (Acosta-Gonzalez et al, 2015). In the passive strategy, known as index tracking, the aim is to reproduce the performance of a chosen benchmark by allocating capital to a subset of assets that represent the index (Mutunge and Haugland, 2018;Wang et al, 2018;Scozzari et al, 2013). As discussed by Wang et al (2018) andSant'Anna et al (2017b), the use of a subset of assets from the benchmark is necessary to deal with the high transaction costs that can negatively impact accumulated returns.…”

“…In the passive strategy, known as index tracking, the aim is to reproduce the performance of a chosen benchmark by allocating capital to a subset of assets that represent the index (Mutunge and Haugland, 2018;Wang et al, 2018;Scozzari et al, 2013). As discussed by Wang et al (2018) andSant'Anna et al (2017b), the use of a subset of assets from the benchmark is necessary to deal with the high transaction costs that can negatively impact accumulated returns. Thus, constraints on the number of assets are incorporated in this type of model (Mutunge and Haugland, 2018), making them computationally infeasible as the number of constituent assets in the benchmark grows.…”

“…Thus, the novel GRASP approaches were compared with CPLEX commercial solver also used for this purpose in the literature portfolio optimization literature (Guastaroba and Speranza, 2012; Lejeune and Samatli‐Pac, 2013; Sant'Anna et al., 2017b). Also, since GAs have great attention of researchers from the portfolio optimization area (Liagkouras and Metaxiotis, 2018a; Kalayci et al., 2019; de Almeida‐Filho et al., 2020), the GRASP approaches were compared with GAs, hybridized with a general‐purpose solver, which have been applied to different index tracking models (Ruiz‐Torrubiano and Suarez, 2009; Wang et al., 2012; Xu et al., 2016; Sant'Anna et al., 2017b; Wang et al., 2018; de Amorim et al., 2021). The hybridization of metaheuristics and a general‐purpose solver makes it possible to solve the associated mixed‐integer index tracking problems without the adoption of solution repairing or constraint handling approaches, as long as this general‐purpose solver can handle the considered constraints (Ruiz‐Torrubiano and Suarez, 2009; Guastaroba and Speranza, 2012; Sant'Anna et al., 2017b; de Amorim et al., 2021).…”

A bi‐level programming framework for identifying optimal parameters in portfolio selection

“…The last category is the stratified sampling (Rudd, 1980;Montfort et al, 2008) and the time-series clustering (Focardi and Fabozzi, 2004;Dose and Cincotti, 2005). Wang et al (2017) proposed a novel portfolio strategy that combines the existing stratified strategy and the optimized sampling strategy through solving a mixed-integer programming model for index tracking. Focardi and Fabozzi (2004) introduced the notion of the distance function and proposed to use time-series clustering to identify assets with similar behaviors.…”