IDEAS home Printed from https://ideas.repec.org/p/gmf/wpaper/2015-15..html
   My bibliography  Save this paper

Portfolio Management With Higher Moments: The Cardinality Impact

Author

Listed:
  • Rui Pedro Brito

    () (Faculty of Economics, University of Coimbra, and GEMF, Portugal)

  • Hélder Sebastião

    () (Faculty of Economics, University of Coimbra, and GEMF, Portugal)

  • Pedro Godinho

    () (Faculty of Economics, University of Coimbra, and GEMF, Portugal)

Abstract

In this paper we extend the study of the cardinality impact from the standard mean-variance scenario to higher moments, considering a utility maximization framework. For each scenario, we propose a bi-objective model that allows the investor to directly analyse the efficient trade-off between expected utility and cardinality. We study not only the effect of cardinality in each scenario but also the real gain of considering higher moments in portfolio management. This analysis is performed assuming that the investor has constant relative risk aversion (CRRA) preferences. For the data collected on the PSI20 index, the empirical results showed that there are no performance gains, in-sample, from the efficient mean-variance expected utility/cardinality portfolios to the efficient expected utility/cardinality portfolios when higher moments are considered. However, the out-of-sample performance of the efficient mean-variance-skewness expected utility/cardinality portfolios and of the efficient mean-variance-skewness-kurtosis expected utility/cardinality portfolios suggest the existence of real gains, especially when transaction costs are considered.

Suggested Citation

  • Rui Pedro Brito & Hélder Sebastião & Pedro Godinho, 2015. "Portfolio Management With Higher Moments: The Cardinality Impact," GEMF Working Papers 2015-15, GEMF, Faculty of Economics, University of Coimbra.
  • Handle: RePEc:gmf:wpaper:2015-15.
    as

    Download full text from publisher

    File URL: http://www.uc.pt/feuc/gemf/working_papers/pdf/2015/gemf_2015-15
    Download Restriction: no

    References listed on IDEAS

    as
    1. Mencía, Javier & Sentana, Enrique, 2009. "Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation," Journal of Econometrics, Elsevier, vol. 153(2), pages 105-121, December.
    2. Fred D. Arditti, 1967. "Risk And The Required Return On Equity," Journal of Finance, American Finance Association, vol. 22(1), pages 19-36, March.
    3. Ledoit, Oliver & Wolf, Michael, 2008. "Robust performance hypothesis testing with the Sharpe ratio," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 850-859, December.
    4. Dimitris Bertsimas & Romy Shioda, 2009. "Algorithm for cardinality-constrained quadratic optimization," Computational Optimization and Applications, Springer, vol. 43(1), pages 1-22, May.
    5. Yacine AÏT‐SAHALI & Michael W. Brandt, 2001. "Variable Selection for Portfolio Choice," Journal of Finance, American Finance Association, vol. 56(4), pages 1297-1351, August.
    6. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    7. Statman, Meir, 1987. "How Many Stocks Make a Diversified Portfolio?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(3), pages 353-363, September.
    8. Chunhachinda, Pornchai & Dandapani, Krishnan & Hamid, Shahid & Prakash, Arun J., 1997. "Portfolio selection and skewness: Evidence from international stock markets," Journal of Banking & Finance, Elsevier, vol. 21(2), pages 143-167, February.
    9. Richard H. Thaler & Shlomo Benartzi, 2001. "Naive Diversification Strategies in Defined Contribution Saving Plans," American Economic Review, American Economic Association, vol. 91(1), pages 79-98, March.
    10. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    11. Andrew L. Turner & Eric J. Weigel, 1992. "Daily Stock Market Volatility: 1928--1989," Management Science, INFORMS, vol. 38(11), pages 1586-1609, November.
    12. Woodside-Oriakhi, M. & Lucas, C. & Beasley, J.E., 2011. "Heuristic algorithms for the cardinality constrained efficient frontier," European Journal of Operational Research, Elsevier, vol. 213(3), pages 538-550, September.
    13. 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..
    14. Campbell Harvey & John Liechty & Merrill Liechty & Peter Muller, 2010. "Portfolio selection with higher moments," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 469-485.
    15. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    16. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. R. P. Brito & H. Sebastião & P. Godinho, 2017. "Portfolio choice with high frequency data: CRRA preferences and the liquidity effect," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 16(2), pages 65-86, August.

    More about this item

    Keywords

    Portfolio management; cardinality; expected utility maximization; CRRA preferences; derivative-free optimization; PSI20 index.;

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:gmf:wpaper:2015-15.. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ana Seiça). General contact details of provider: http://edirc.repec.org/data/cebucpt.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.