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Three fuzzy goal programming models for index portfolios

Author

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  • Liang-chuan Wu

    (National Chung Hsing University, Taichung, Taiwan R.O.C)

  • I-chan Tsai

    (National Chung Hsing University, Taichung, Taiwan R.O.C)

Abstract

Studies show that most actively managed mutual funds struggle to beat the market, driving an increase in the popularity of index investing. Index investing instruments, including index funds and Exchange-traded Funds, aim to track market performance. This study pursues both tracking error minimization and excess return maximization, two conflicting objectives, to construct an index portfolio. In the real-world financial environment, the desires and expectations of decision makers are generally imprecise. This study applies fuzzy theory to deal with imprecise objectives. This study represents minimizing tracking error and maximizing excess return as ‘fuzzy goals’ to improve traditional goal programming, which is suitable for handling multiple conflicting objectives, but subject to establishing crisp goals. Three fuzzy goal programming (FGP) models that track indexes are compared and discussed, and the results show that through certain membership functions and tracking models, an index tracking portfolio with a tracking error lower than the 0050 index fund, and a similar excess return to 0050 index fund can be constructed using additive type FGP. max-min type FGP underperforms the additive type FGP in index fund construction.

Suggested Citation

  • Liang-chuan Wu & I-chan Tsai, 2014. "Three fuzzy goal programming models for index portfolios," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(8), pages 1155-1169, August.
    • Handle: RePEc:pal:jorsoc:v:65:y:2014:i:8:p:1155-1169
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    References listed on IDEAS

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    3. Huimin Peng, 2020. "Holding-Based Evaluation upon Actively Managed Stock Mutual Funds in China," Papers 2004.05322, arXiv.org, revised Jul 2020.
    4. Julio Cezar Soares Silva & Adiel Teixeira de Almeida Filho, 2023. "A systematic literature review on solution approaches for the index tracking problem in the last decade," Papers 2306.01660, arXiv.org, revised Jun 2023.

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