A heuristic framework for the bi-objective enhanced index tracking problem

Filippi, Carlo; Guastaroba, Gianfranco; Speranza, Maria

doi:10.1016/j.omega.2016.01.004

Cited by 58 publications

(34 citation statements)

References 51 publications

(85 reference statements)

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“…Their model includes, among other features, a cardinality constraint and buy-in threshold limits, and is solved by means of an immunitybased multi-objective algorithm. Filippi et al [6] cast the EITP as a bi-objective MILP model with several real features, including a cardinality constraint and buy-in threshold limits on the shares. Their optimization model aims at maximizing the excess return of the portfolio over the benchmark, while minimizing the tracking error, as measured by the absolute deviation between the portfolio and benchmark values.…”

Section: Recent Literature On the Enhanced Index Tracking Problemmentioning

confidence: 99%

Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem

Guastaroba

Mansini

Ogryczak

et al. 2016

European Journal of Operational Research

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Modern performance measures differ from the classical ones since they assess the performance against a benchmark and usually account for asymmetry in return distributions. The Omega ratio is one of these measures. Until recently, limited research has addressed the optimization of the Omega ratio since it has been thought to be computationally intractable. The Enhanced Index Tracking Problem (EITP) is the problem of selecting a portfolio of securities able to outperform a market index while bearing a limited additional risk. In this paper, we propose two novel mathematical formulations for the EITP based on the Omega ratio. The first formulation applies a standard definition of the Omega ratio where it is computed with respect to a given value, whereas the second formulation considers the Omega ratio with respect to a random target. We show how each formulation, nonlinear in nature, can be transformed into a Linear Programming model. We further extend the models to include real features, such as a cardinality constraint and buy-in thresholds on the investments, obtaining Mixed Integer Linear Programming problems. Computational results conducted on a large set of benchmark instances show that the portfolios selected by the model assuming a standard definition of the Omega ratio are consistently outperformed, in terms of out-of-sample performance, by those obtained solving the model that considers a random target. Furthermore, in most of the instances the portfolios optimized with the latter model mimic very closely the behavior of the benchmark over the out-of-sample period, while yielding, sometimes, significantly larger returns.

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Section: Recent Literature On the Enhanced Index Tracking Problemmentioning

confidence: 99%

Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem

Guastaroba

Mansini

Ogryczak

et al. 2016

European Journal of Operational Research

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“…Canakgoz and Beasley (2009) review the differences between EIM and IRM. EIM chases excess returns when minimizing tracking errors (Roman et al, 2013;Filippi et al, 2016).…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…There is one strand of literature that treats EIM as a multi-objective decision model. For example, Filippi et al (2016) and Wu et al (2007) convert EIM to a bi-objective model, Anagnostopoulos and Mamanis (2010) and Hirschberger et al (2013) convert it to a tri-objective model. However, the issue here is that the optimal solution set to a multi-objective optimization typically has very high or even infinite dimensional cardinality.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…Appel et al (2016) report that the proportion of total market capitalization of indexation funds quadrupled from 2% to more than 8%. Among indexation products, enhanced index tracking funds that operate according to trade-offs between tracking errors and excess returns have developed more quickly than index replication funds (Filippi et al, 2016). These index-linked trades have become especially prevalent in the asset management industry, as investors tend to require benchmarking as a mechanism to evaluate portfolio performance.…”

Section: Introductionmentioning

confidence: 99%

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Index tracking model, downside risk and non-parametric kernel estimation

Huang

Yao

2018

Journal of Economic Dynamics and Control

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In this paper, we propose an index tracking model with the conditional value-at-risk (CVaR) constraint based on a non-parametric kernel (NPK) estimation framework. In theory, we demonstrate that the index tracking model with the CVaR constraint is a convex optimization problem. We then derive NPK estimators for tracking errors and CVaR, and thereby construct the NPK index tracking model. Monte Carlo simulations show that the NPK method outperforms the linear programming (LP) method in terms of estimation accuracy. In addition, the NPK method can enhance computational efficiency when the sample size is large. Empirical tests show that the NPK method can effectively control downside risk and obtain higher excess returns, in both bearish and bullish market environments.

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“…Bruni et al (2015) model the EITP as a bi-objective linear program that maximizes the average excess return of the portfolio over the benchmark, and minimizes the maximum downside deviation of the portfolio return from the market index. Filippi et al (2016) cast the EITP as a bi-objective mixed-integer LP model which maximizes the excess return of the portfolio over the benchmark, and minimizes the tracking error, here defined as the absolute deviation between the portfolio and benchmark values. The authors devise a bi-objective heuristic framework for its solution.…”

Section: Introductionmentioning

confidence: 99%

Enhanced index tracking with CVaR-based ratio measures

et al. 2020

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The enhanced index tracking problem (EITP) calls for the determination of an optimal portfolio of assets with the bi-objective of maximizing the excess return of the portfolio above a benchmark and minimizing the tracking error. The EITP is capturing a growing attention among academics, both for its practical relevance and for the scientific challenges that its study, as a multi-objective problem, poses. Several optimization models have been proposed in the literature, where the tracking error is measured in terms of standard deviation or in linear form using, for instance, the mean absolute deviation. More recently, reward-risk optimization measures, like the Omega ratio, have been adopted for the EITP. On the other side, shortfall or quantile risk measures have nowadays gained an established popularity in a variety of financial applications. In this paper, we propose a class of bi-criteria optimization models for the EITP, where risk is measured using the weighted multiple conditional value-at-risk (WCVaR). The WCVaR is defined as a weighted combination of multiple CVaR measures, and thus allows a more detailed risk aversion modeling compared to the use of a single CVaR measure. The application of the WCVaR to the EITP is analyzed, both theoretically and empirically. Through extensive computational experiments, the performance of the optimal portfolios selected by means of the proposed optimization models is compared, both in-sample and, more importantly, out-of-sample, to the one of the portfolios obtained using another recent optimization model taken from the literature. KeywordsEnhanced index tracking · Quantile risk measures · Conditional value-at-risk · Mean-risk models · Risk-reward ratios · Risk-averse optimization · Stochastic dominance · Linear programming Annals of Operations ResearchSortino ratio (see Sortino and Price 1994) are widely used to evaluate, compare and rank different investment strategies. To the best of our knowledge, Meade and Beasley (2011) are the first ones attempting to use a reward-risk ratio in the context of enhanced indexation. The authors introduce a non-linear optimization model, based on the maximization of a modified Sortino ratio, and solve it by means of a genetic algorithm. However, the non-linearity of this model may represent an undesirable limitation to its use in financial practice, especially when portfolios have to meet several side constraints (such as cardinality constraints or buy-in thresholds) or when large-scale instances have to be solved since, in most cases, the inclusion of these features requires the introduction of binary and integer variables (see the survey by Mansini et al. 2014). Based on this observation, Guastaroba et al. (2016) introduce two mathematical formulations for the EITP based on the Omega ratio. The Omega ratio is a performance measure introduced by Keating and Shadwick (2002) which, broadly speaking, can be defined as the ratio between expected value of the profits, defined as the portfolio returns over a predetermined target τ , and e...

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A heuristic framework for the bi-objective enhanced index tracking problem

Cited by 58 publications

References 51 publications

Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem

Linear programming models based on Omega ratio for the Enhanced Index Tracking Problem

Index tracking model, downside risk and non-parametric kernel estimation

Enhanced index tracking with CVaR-based ratio measures

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