A linear model for tracking error minimization

Rudolf, Markus; Wolter, Hans-Jürgen; Zimmermann, Heinz

doi:10.1016/s0378-4266(98)00076-4

Cited by 165 publications

(90 citation statements)

References 9 publications

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“…They also show that linear tracking error optimization is equivalent to expected utility maximization and lower partial moment minimization. This study is closely related to the last work of Rudolf et al (1999). We propose a robust optimization approach and compare different models using recent data sets (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011).…”

Section: Introductionmentioning

confidence: 91%

“…Similar to Rudolf et al (1999) the objective function is to minimize some function of tracking error over stock weights, β. Typically, the deviation between the tracking portfolio and the index is defined as Equation 1:…”

Section: Mean Square Formulationmentioning

confidence: 99%

“…Their tractable robust framework controls conservatism of the solution which protects against worst-case realizations of potential estimation errors and other deviations. Rudolf et al (1999) propose four linear models for minimizing the tracking error between the returns of a portfolio and a benchmark. Their idea of linearization is based on the fact that in the real market we confront with linear performance fees of fund managers; therefore, they argue that linear deviations give a more accurate description of the investors risk attitude rather than squared deviations.…”

Section: Introductionmentioning

confidence: 99%

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A Robust Optimization Approach for Index Tracking Problem

Gharakhani¹,

Fazlelahi²,

Sadjadi³

2014

Journal of Computer Science

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Index tracking is an investment approach where the primary objective is to keep portfolio return as close as possible to a target index without purchasing all index components. The main purpose is to minimize the tracking error between the returns of the selected portfolio and a benchmark. In this study, quadratic as well as linear models are presented for minimizing the tracking error. The uncertainty is considered in the input data using a tractable robust framework that controls the level of conservatism while maintaining linearity. The linearity of the proposed robust optimization models allows a simple implementation of an ordinary optimization software package to find the optimal robust solution. The proposed model of this study employs Morgan Stanley Capital International Index as the target index and the results are reported for six national indices including Japan, the USA, the UK, Germany, Switzerland and France. The performance of the proposed models is evaluated using several financial criteria e.g., information ratio, market ratio, Sharpe ratio and Treynor ratio. The preliminary results demonstrate that the proposed model lowers the amount of tracking error while raising values of portfolio performance measures.

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Section: Introductionmentioning

confidence: 91%

Section: Mean Square Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Robust Optimization Approach for Index Tracking Problem

Gharakhani¹,

Fazlelahi²,

Sadjadi³

2014

Journal of Computer Science

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“…Rudolf, Wolter and Zimmermann [9] used linear deviations instead of squared deviations to give four definitions of the linear tracking errors. We adopt the tracking error based on the mean absolute downside deviations to formulate the index tracking portfolio selection model in this paper.…”

Section: Bi-objective Programming Model For Index Tracking Portfoliomentioning

confidence: 99%

“…Clarke, Krase and Statman [2] defined a linear tracking error which is the absolute deviation between the managed portfolio return and the benchmark portfolio return. Based on the linear objective function in which absolute deviations between portfolio and benchmark returns are used, Rudolf, Wolter and Zimmermann [9] proposed four alternative definitions of a tracking error. Furthermore, they gave four linear optimization models for index tracking portfolio selection problem.…”

Section: Introductionmentioning

confidence: 99%

A Fuzzy Index Tracking Portfolio Selection Model

Fang

Wang

2005

Lecture Notes in Computer Science

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Abstract. The investment strategies can be divided into two classes: passive investment strategies and active investment strategies. An index tracking investment strategy belongs to the class of passive investment strategies. The index tracking error and the excess return are considered as two objective functions, a bi-objective programming model is proposed for the index tracking portfolio selection problem. Furthermore, based on fuzzy decision theory, a fuzzy index tracking portfolio selection model is also proposed. A numerical example is given to illustrate the behavior of the proposed fuzzy index tracking portfolio selection model.

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Hedge Funds

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A linear model for tracking error minimization

Cited by 165 publications

References 9 publications

A Robust Optimization Approach for Index Tracking Problem

A Robust Optimization Approach for Index Tracking Problem

A Fuzzy Index Tracking Portfolio Selection Model

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