An evolutionary heuristic for the index tracking problem

Beasley, John E.; Meade, Nigel; Chang, Tun-Jen

doi:10.1016/s0377-2217(02)00425-3

Cited by 283 publications

(187 citation statements)

References 40 publications

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“…The idea is that a portfolio that yielded in the past performance levels close to those of the benchmark will continue to do so in the future. The (total or average) squared deviation is one of the most popular tracking measures [5,28,38,76]. Other tracking metrics minimize the tracking error variance, the mean absolute deviation, the root squared mean error, and a power function of deviation (see [38] for a detailed discussion of the most popular tracking measures).…”

Section: Stochastic Index Tracking Modelmentioning

confidence: 99%

“…For instance, the price to pay for the full replication of the Russell 2000 index is estimated at 1.3% and 1.84% annually. 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].…”

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confidence: 99%

“…Multiple models and algorithmic techniques have been proposed for their construction. A comprehensive review of the literature (until 2003) can be found in [5]. Below, we review a number of more recent index tracking studies, starting with traditional index funds before moving to the enhanced indexation literature.…”

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confidence: 99%

“…An evolutionary heuristic [5], a clustering approach [37], and a Lagrangian relaxation method used within a branch-and-bound algorithm [85] are employed to construct an index fund from an asset universe containing 225 (in [5]) and 500 (in [85]) securities. 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].…”

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confidence: 99%

“…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]).…”

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confidence: 99%

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Construction of Risk-Averse Enhanced Index Funds

Lejeune

Samatlı-Paç

2013

INFORMS Journal on Computing

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We propose a partial replication strategy to construct risk-averse enhanced index funds. Our model takes into account the parameter estimation risk by defining the asset returns and the return covariance terms as random variables. The variance of the index fund return is forced to be below a low-risk threshold with a large probability, thereby limiting the market risk exposure of the investors and the moral hazard associated with the wage structure of fund managers. The resulting stochastic integer problem is reformulated through the derivation of a deterministic equivalent for the risk constraint and the use of a block decomposition technique. We develop an exact outer approximation method based on the relaxation of some binary restrictions and the reformulation of the cardinality constraint. The method provides a hierarchical organization of the computations with expanding sets of integer-restricted variables and outperforms the Bonmin and the Cplex 12.1 solvers. The method can solve very large (up to 1000 securities) instances, converges fast, scales well, and is general enough to be applicable to problems with buy-in threshold constraints. Cross-validation tests show that the constructed funds track closely and are consistently less risky than the benchmark on the out-of-sample period.

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