IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-04134833.html
   My bibliography  Save this paper

Risk-Adjusted Performance And Semi-Moments Of Non-Gaussian Portfolio Returns Distributions

Author

Listed:
  • Jules Sadefo Kamdem

    (MRE - Montpellier Recherche en Economie - UM - Université de Montpellier)

Abstract

In this paper, we find analytic expressions of the lower partial moment and kappa index of linear portfolios when the returns are elliptically distributed. We also introduced the notion of Target Semi-Kurtosis of portfolio return and discuss the robust optimization Mean-LPM problem with non- gaussian risk factors. Special attention is given to the particular case of a mixture of multivariate t-distributions with application for portfolio allocation of some ESG indices and the CAC 40 index.

Suggested Citation

  • Jules Sadefo Kamdem, 2023. "Risk-Adjusted Performance And Semi-Moments Of Non-Gaussian Portfolio Returns Distributions," Working Papers hal-04134833, HAL.
    • Handle: RePEc:hal:wpaper:hal-04134833
    Note: View the original document on HAL open archive server: https://hal.science/hal-04134833
    as

    Download full text from publisher

    File URL: https://hal.science/hal-04134833/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Trino-Manuel Ñíguez & Ivan Paya & David Peel & Javier Perote, 2019. "Flexible distribution functions, higher-order preferences and optimal portfolio allocation," Quantitative Finance, Taylor & Francis Journals, vol. 19(4), pages 699-703, April.
    2. Michael Stutzer, 2011. "Portfolio choice with endogenous utility: a large deviations approach," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 43, pages 619-640, World Scientific Publishing Co. Pte. Ltd..
    3. Breitmeyer, Carsten & Hakenes, Hendrik & Pfingsten, Andreas, 2004. "From poverty measurement to the measurement of downside risk," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 327-348, May.
    4. M. Ryan Haley & Harry J. Paarsch & Charles H. Whiteman, 2013. "Smoothed safety first and the holding of assets," Quantitative Finance, Taylor & Francis Journals, vol. 13(2), pages 167-176, January.
    5. Valeri Zakamouline, 2014. "Portfolio performance evaluation with loss aversion," Quantitative Finance, Taylor & Francis Journals, vol. 14(4), pages 699-710, April.
    6. Buckley, Ian & Saunders, David & Seco, Luis, 2008. "Portfolio optimization when asset returns have the Gaussian mixture distribution," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1434-1461, March.
    7. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
    8. Laurent El Ghaoui & Maksim Oks & Francois Oustry, 2003. "Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach," Operations Research, INFORMS, vol. 51(4), pages 543-556, August.
    9. Bawa, Vijay S., 1978. "Safety-First, Stochastic Dominance, and Optimal Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(2), pages 255-271, June.
    10. M. Ryan Haley & M. Kevin McGee & Todd B. Walker, 2013. "Disparity, Shortfall, and Twice-Endogenous HARA Utility," Econometric Reviews, Taylor & Francis Journals, vol. 32(4), pages 524-541, December.
    11. Eling, Martin & Schuhmacher, Frank, 2007. "Does the choice of performance measure influence the evaluation of hedge funds?," Journal of Banking & Finance, Elsevier, vol. 31(9), pages 2632-2647, September.
    12. D. Goldfarb & G. Iyengar, 2003. "Robust Portfolio Selection Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 1-38, February.
    13. Kirby, Chris & Ostdiek, Barbara, 2012. "It’s All in the Timing: Simple Active Portfolio Strategies that Outperform Naïve Diversification," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(2), pages 437-467, April.
    14. Unser, Matthias, 2000. "Lower partial moments as measures of perceived risk: An experimental study," Journal of Economic Psychology, Elsevier, vol. 21(3), pages 253-280, June.
    15. León, Angel & Navarro, Lluís & Nieto, Belén, 2019. "Screening rules and portfolio performance," The North American Journal of Economics and Finance, Elsevier, vol. 48(C), pages 642-662.
    16. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    17. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    18. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    19. M. Ryan Haley, 2016. "Shortfall minimization and the Naive (1/N) portfolio: an out-of-sample comparison," Applied Economics Letters, Taylor & Francis Journals, vol. 23(13), pages 926-929, September.
    20. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
    21. Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Capital market equilibrium in a mean-lower partial moment framework," Journal of Financial Economics, Elsevier, vol. 5(2), pages 189-200, November.
    22. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    23. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jules Sadefo-Kamdem, 2011. "Downside Risk And Kappa Index Of Non-Gaussian Portfolio With Lpm," Working Papers hal-00733043, HAL.
    2. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    3. Shushang Zhu & Duan Li & Shouyang Wang, 2009. "Robust portfolio selection under downside risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 869-885.
    4. Lwin, Khin T. & Qu, Rong & MacCarthy, Bart L., 2017. "Mean-VaR portfolio optimization: A nonparametric approach," European Journal of Operational Research, Elsevier, vol. 260(2), pages 751-766.
    5. León, Angel & Moreno, Manuel, 2017. "One-sided performance measures under Gram-Charlier distributions," Journal of Banking & Finance, Elsevier, vol. 74(C), pages 38-50.
    6. Robert Jarrow & Feng Zhao, 2006. "Downside Loss Aversion and Portfolio Management," Management Science, INFORMS, vol. 52(4), pages 558-566, April.
    7. Zhangxin (Frank) Liu & Michael J. O'Neill, 2018. "Partial moment volatility indices," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 58(1), pages 195-215, March.
    8. Anthonisz, Sean A., 2012. "Asset pricing with partial-moments," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 2122-2135.
    9. Kocuk, Burak & Cornuéjols, Gérard, 2020. "Incorporating Black-Litterman views in portfolio construction when stock returns are a mixture of normals," Omega, Elsevier, vol. 91(C).
    10. Li Chen & Simai He & Shuzhong Zhang, 2011. "Tight Bounds for Some Risk Measures, with Applications to Robust Portfolio Selection," Operations Research, INFORMS, vol. 59(4), pages 847-865, August.
    11. Ling, Aifan & Sun, Jie & Yang, Xiaoguang, 2014. "Robust tracking error portfolio selection with worst-case downside risk measures," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 178-207.
    12. Hildebrandt, Patrick & Knoke, Thomas, 2011. "Investment decisions under uncertainty--A methodological review on forest science studies," Forest Policy and Economics, Elsevier, vol. 13(1), pages 1-15, January.
    13. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    14. Kaplanski, Guy & Kroll, Yoram, 2002. "VaR Risk Measures versus Traditional Risk Measures: an Analysis and Survey," MPRA Paper 80070, University Library of Munich, Germany.
    15. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Sean A. Anthonisz & Tālis J. Putniņš, 2017. "Asset Pricing with Downside Liquidity Risks," Management Science, INFORMS, vol. 63(8), pages 2549-2572, August.
    17. Gonzalo, Jesús & Olmo, José, 2008. "Testing downside risk efficiency under market distress," UC3M Working papers. Economics we084321, Universidad Carlos III de Madrid. Departamento de Economía.
    18. Caporin, Massimiliano & Costola, Michele & Jannin, Gregory & Maillet, Bertrand, 2018. "“On the (Ab)use of Omega?”," Journal of Empirical Finance, Elsevier, vol. 46(C), pages 11-33.
    19. Georges Hübner & Thomas Lejeune, 2015. "Portfolio choice and investor preferences : A semi-parametric approach based on risk horizon," Working Paper Research 289, National Bank of Belgium.
    20. M. Haley, 2014. "Gaussian and logistic adaptations of smoothed safety first," Annals of Finance, Springer, vol. 10(2), pages 333-345, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-04134833. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.