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Portfolio optimization for student t and skewed t returns


  • Wenbo Hu
  • Alec Kercheval


It is well-established that equity returns are not Normally distributed, but what should the portfolio manager do about this, and is it worth the effort? It is now feasible to employ better multivariate distribution families that capture heavy tails and skewness in the data; we argue that among the best are the Student t and skewed t distributions. These can be efficiently fitted to data, and show a much better fit to real returns than the Normal distribution. By examining efficient frontiers computed using different distributional assumptions, we show, using for illustration five stocks chosen from the Dow index, that the choice of distribution has a significant effect on how much available return can be captured by an optimal portfolio on the efficient frontier.

Suggested Citation

  • Wenbo Hu & Alec Kercheval, 2010. "Portfolio optimization for student t and skewed t returns," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 91-105.
  • Handle: RePEc:taf:quantf:v:10:y:2010:i:1:p:91-105
    DOI: 10.1080/14697680902814225

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    Cited by:

    1. Gürtler, Marc & Rauh, Ronald, 2012. "Challenging traditional risk models by a non-stationary approach with nonparametric heteroscedasticity," Working Papers IF41V1, Technische Universität Braunschweig, Institute of Finance.
    2. Gautier Marti & S'ebastien Andler & Frank Nielsen & Philippe Donnat, 2016. "Clustering Financial Time Series: How Long is Enough?," Papers 1603.04017,, revised Apr 2016.
    3. Mainik, Georg & Mitov, Georgi & Rüschendorf, Ludger, 2015. "Portfolio optimization for heavy-tailed assets: Extreme Risk Index vs. Markowitz," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 115-134.
    4. repec:eee:apmaco:v:282:y:2016:i:c:p:187-203 is not listed on IDEAS
    5. Daniel T. Cassidy & Michael J. Hamp & Rachid Ouyed, 2010. "Student's t-Distribution Based Option Sensitivities: Greeks for the Gosset Formulae," Papers 1003.1344,, revised Jul 2010.
    6. Gautier Marti & Sébastien Andler & Frank Nielsen & Philippe Donnat, 2016. "Clustering Financial Time Series: How Long is Enough?," Post-Print hal-01400395, HAL.
    7. repec:gam:jrisks:v:5:y:2017:i:2:p:27-:d:97820 is not listed on IDEAS
    8. repec:eee:joecas:v:16:y:2017:i:c:p:26-41 is not listed on IDEAS
    9. repec:spr:joptap:v:161:y:2014:i:1:d:10.1007_s10957-013-0348-y is not listed on IDEAS
    10. Daniel T. Cassidy & Michael J. Hamp & Rachid Ouyed, 2013. "Log Student’s t -distribution-based option sensitivities: Greeks for the Gosset formulae," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1289-1302, July.
    11. Seyedehzahra NEMATOLLAHI & Giancarlo MANZI, 2018. "Portfolio Management Using Prospect Theory: Comparing Genetic Algorithms and Particle Swarm Optimization," Departmental Working Papers 2018-03, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    12. Jondeau, Eric, 2016. "Asymmetry in tail dependence in equity portfolios," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 351-368.
    13. González-Pedraz, Carlos & Moreno, Manuel & Peña, Juan Ignacio, 2014. "Tail risk in energy portfolios," Energy Economics, Elsevier, vol. 46(C), pages 422-434.
    14. Michele Leonardo Bianchi & Gian Luca Tassinari & Frank J. Fabozzi, 2016. "Riding With The Four Horsemen And The Multivariate Normal Tempered Stable Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-28, June.


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