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Portfolio selection with skewness: A comparison of methods and a generalized one fund result

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  • Briec, Walter
  • Kerstens, Kristiaan
  • Van de Woestyne, Ignace

Abstract

This contribution compares existing and newly developed techniques for geometrically representing mean–variance–skewness portfolio frontiers based on the rather widely adapted methodology of polynomial goal programming (PGP) on the one hand and the more recent approach based on the shortage function on the other hand. Moreover, we explain the working of these different methodologies in detail and provide graphical illustrations in relation to the goal programming literature in operations research. Inspired by these illustrations, we prove two new results: a formal relation between both approaches and a generalization of the well-known one fund separation theorem from traditional mean–variance portfolio theory.

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  • Briec, Walter & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2013. "Portfolio selection with skewness: A comparison of methods and a generalized one fund result," European Journal of Operational Research, Elsevier, vol. 230(2), pages 412-421.
    • Handle: RePEc:eee:ejores:v:230:y:2013:i:2:p:412-421
    DOI: 10.1016/j.ejor.2013.04.021
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    2. Lassance, Nathan, 2022. "Reconciling mean-variance portfolio theory with non-Gaussian returns," European Journal of Operational Research, Elsevier, vol. 297(2), pages 729-740.
    3. Kerstens, Kristiaan & Mazza, Paolo & Ren, Tiantian & Van de Woestyne, Ignace, 2022. "Multi-Time and Multi-Moment Nonparametric Frontier-Based Fund Rating: Proposal and Buy-and-Hold Backtesting Strategy," Omega, Elsevier, vol. 113(C).
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    7. Lassance, Nathan & Vrins, Frédéric, 2021. "Portfolio selection with parsimonious higher comoments estimation," Journal of Banking & Finance, Elsevier, vol. 126(C).
    8. Lassance, Nathan & Vrins, Frédéric, 2019. "Robust portfolio selection using sparse estimation of comoment tensors," LIDAM Discussion Papers LFIN 2019007, Université catholique de Louvain, Louvain Finance (LFIN).
    9. Vohra, Suprita & Fabozzi, Frank J., 2019. "Effectiveness of developed and emerging market FX options in active currency risk management," Journal of International Money and Finance, Elsevier, vol. 96(C), pages 130-146.
    10. Massimiliano Kaucic & Roberto Daris, 2015. "Multi-Objective Stochastic Optimization Programs for a Non-Life Insurance Company under Solvency Constraints," Risks, MDPI, vol. 3(3), pages 1-30, September.
    11. Farshad Noravesh & Kristiaan Kerstens, 2022. "Some connections between higher moments portfolio optimization methods," Papers 2201.00205, arXiv.org.
    12. Brandouy, Olivier & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2015. "Frontier-based vs. traditional mutual fund ratings: A first backtesting analysis," European Journal of Operational Research, Elsevier, vol. 242(1), pages 332-342.
    13. Adrian Gepp & Geoff Harris & Bruce Vanstone, 2020. "Financial applications of semidefinite programming: a review and call for interdisciplinary research," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 60(4), pages 3527-3555, December.
    14. Dong, Xiaohui & Wang, Ming & Zhong, Guang-Yan & Yang, Fengzao & Duan, Weilong & Li, Jiang-Cheng & Xiong, Kezhao & Zeng, Chunhua, 2018. "Stochastic delayed kinetics of foraging colony system under non-Gaussian noise," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 1-13.

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    More about this item

    Keywords

    Shortage function; PGP; Efficient frontier; Mean–variance; Mean–variance–skewness;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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