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Portfolio selection in multidimensional general and partial moment space

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  • W. Briec
  • K. Kerstens

    (UMR CNRS 8179 - Université de Lille, Sciences et Technologies - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper develops a general approach for the single period portfolio optimization problem in a multidimensional general and partial moment space. A shortage function is defined that looks for possible increases in odd moments and decreases in even moments. A main result is that this shortage function ensures sufficient conditions for global optimality. It also forms a natural basis for developing tests on the influence of additional moments. Furthermore, a link is made with an approximation of an arbitrary order of a general indirect utility function. This non-parametric efficiency measurement framework permits to differentiate mainly between portfolio efficiency and allocative efficiency. Finally, information can, in principle, be inferred about the revealed risk aversion, prudence, temperance and other higher-order risk characteristics of investors.
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Suggested Citation

  • W. Briec & K. Kerstens, 2010. "Portfolio selection in multidimensional general and partial moment space," Post-Print halshs-00473219, HAL.
    • Handle: RePEc:hal:journl:halshs-00473219
    DOI: 10.1016/j.jedc.2009.11.001
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    2. 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.
    3. Gomez-Gonzalez, Jose Eduardo & Hirs-Garzon, Jorge & Uribe, Jorge M., 2020. "Spillovers beyond the variance: exploring the natural gas and oil higher order risk linkages with the global financial markets," Working papers 46, Red Investigadores de Economía.
    4. 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).
    5. K Kerstens & I Van de Woestyne, 2011. "Negative data in DEA: a simple proportional distance function approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1413-1419, July.
    6. Gan, Quan, 2014. "Location-scale portfolio selection with factor-recentered skew normal asset returns," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 176-187.
    7. Kerstens, Kristiaan & Mounir, Amine & de Woestyne, Ignace Van, 2011. "Non-parametric frontier estimates of mutual fund performance using C- and L-moments: Some specification tests," Journal of Banking & Finance, Elsevier, vol. 35(5), pages 1190-1201, May.
    8. Lamb, John D. & Tee, Kai-Hong, 2012. "Data envelopment analysis models of investment funds," European Journal of Operational Research, Elsevier, vol. 216(3), pages 687-696.
    9. Lamb, John D. & Tee, Kai-Hong, 2012. "Resampling DEA estimates of investment fund performance," European Journal of Operational Research, Elsevier, vol. 223(3), pages 834-841.
    10. Massol, Olivier & Banal-Estañol, Albert, 2014. "Export diversification through resource-based industrialization: The case of natural gas," European Journal of Operational Research, Elsevier, vol. 237(3), pages 1067-1082.
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    12. Kerstens, Kristiaan & Mounir, Amine & Van de Woestyne, Ignace, 2010. "Benchmarking Mean-Variance Portfolios. Using a Shortage Function: The Choice of Direction Vector," Working Papers 2010/01, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    13. Babalos, Vassilios & Mamatzakis, Emmanuel C. & Matousek, Roman, 2015. "The performance of US equity mutual funds," Journal of Banking & Finance, Elsevier, vol. 52(C), pages 217-229.
    14. Jin, Qianying & Basso, Antonella & Funari, Stefania & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2024. "Evaluating different groups of mutual funds using a metafrontier approach: Ethical vs. non-ethical funds," European Journal of Operational Research, Elsevier, vol. 312(3), pages 1134-1145.
    15. Andreu, Laura & Serrano, Miguel & Vicente, Luis, 2019. "Efficiency of mutual fund managers: A slacks-based manager efficiency index," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1180-1193.
    16. Massimiliano Caporin & Grégory M. Jannin & Francesco Lisi & Bertrand B. Maillet, 2014. "A Survey On The Four Families Of Performance Measures," Journal of Economic Surveys, Wiley Blackwell, vol. 28(5), pages 917-942, December.
    17. Tarnaud, Albane Christine & Leleu, Hervé, 2018. "Portfolio analysis with DEA: Prior to choosing a model," Omega, Elsevier, vol. 75(C), pages 57-76.
    18. Krüger, Jens, 2021. "Nonparametric Portfolio Efficiency Measurement with Higher Moments," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 130825, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    19. 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.
    20. Gomez-Gonzalez, Jose E. & Hirs-Garzon, Jorge & Uribe, Jorge M., 2022. "Spillovers beyond the variance: Exploring the higher order risk linkages between commodity markets and global financial markets," Journal of Commodity Markets, Elsevier, vol. 28(C).
    21. Chen, J.J. & Wu, Q.H. & Zhang, L.L. & Wu, P.Z., 2017. "Multi-objective mean–variance–skewness model for nonconvex and stochastic optimal power flow considering wind power and load uncertainties," European Journal of Operational Research, Elsevier, vol. 263(2), pages 719-732.
    22. Emmanuel Jurczenko & Bertrand Maillet & Paul Merlin, 2008. "Efficient Frontier for Robust Higher-order Moment Portfolio Selection," Post-Print halshs-00336475, HAL.
    23. Briec, Walter & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2011. "Portfolio Selection with Skewness: A Comparison and a Generalized Two Fund Separation Result," Working Papers 2011/09, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    24. Xiaochun Meng & James W. Taylor & Souhaib Ben Taieb & Siran Li, 2020. "Scores for Multivariate Distributions and Level Sets," Papers 2002.09578, arXiv.org, revised Jun 2023.
    25. 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.

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    More about this item

    Keywords

    Shortage function Efficient frontier K-moment portfolios;

    JEL classification:

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

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