A hybrid optimization approach to index tracking

Abstract

Index tracking consists in reproducing the performance of a stock-market index by investing in a subset of the stocks included in the index. A hybrid strategy that combines an evolutionary algorithm with quadratic programming is designed to solve this NP-hard problem: Given a subset of assets, quadratic programming yields the optimal tracking portfolio that invests only in the selected assets. The combinatorial problem of identifying the appropriate assets is solved by a genetic algorithm that uses the output of the quadratic optimization as fitness function. This hybrid approach allows the identification of quasi-optimal tracking portfolios at a reduced computational cost.

Portfolio optimization and index tracking for the shipping stock and freight markets using evolutionary algorithms

“…The DE algorithm has also been used in other recent studies using hybrid and multi-objective schemes Krink and Paterlini, 2011), as well as in the context of loss aversion (Maringer, 2008) and mutual fund replication (Zhang and Maringer, 2010). Other recently proposed algorithmic procedures include immune systems (Li et al, 2011), hybrid algorithms (Ruiz-Torrubiano and Suárez, 2009;Scozzari et al 2012), robust optimization (Chen and Kwon, 2012) and mixed-integer programming formulations (Canakgoz and Beasley, 2008;Stoyan and Kwon, 2010). An overview of different methods can be found in Woodside-Oriakhi et al (2011).…”

Construction of Risk-Averse Enhanced Index Funds

“…These well-documented issues [5,12,18,28,29,31] hamper the use of a full replication approach and explain the success of partial replication approaches. Partial replication means that the fund manager is allowed to invest in a limited number of securities to track the benchmark [5,8,28,38,66,69,80]. The requirement is enforced through the use of binary decision variables and the introduction of a cardinality constraint.…”

“…The index fund is built with a differential evolution search heuristic in [55,66]. A genetic algorithm determines the amount to be invested in the assets included in the index fund in [76], while Ruiz-Torrubiano and Suarez [80] develop a genetic algorithm to select the assets and solve a quadratic programming problem to define the size of the positions. Two weighted components representing the tracking error variance and the number of assets in the index are included in the objective function in [25,46].…”

“…He empirically shows that derivatives-based EIFs are those that have the risk profile most closely resembling that of the benchmark. Note that many of the index fund studies [5,33,18,46,55,66,76,80,92] use heuristic methods and model the future asset returns as deterministic parameters. The presence of a cardinality constraint and integer variables, a key feature and source of complexity for the partial replication index problem, arise in other types of financial optimization problems (see, e.g., [9,15,21,47]).…”

Construction of Risk-Averse Enhanced Index Funds

“…The mean squared tracking error is minimized and asset universes comprising respectively 225, 65, 30 and 225 assets are analyzed in [55,66,76,80]. The index fund is built with a differential evolution search heuristic in [55,66].…”