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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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    References listed on IDEAS

    1. Kjersti Aas & Ingrid Hobaek Haff, 2006. "The Generalized Hyperbolic Skew Student's t-Distribution," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 275-309.
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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. Trabelsi, Nader, 2017. "Asymmetric tail dependence between oil price shocks and sectors of Saudi Arabia System," The Journal of Economic Asymmetries, Elsevier, vol. 16(C), pages 26-41.
    3. John R. Birge & Luis Chavez-Bedoya, 2016. "Portfolio optimization under a generalized hyperbolic skewed t distribution and exponential utility," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1019-1036, July.
    4. Jondeau, Eric, 2016. "Asymmetry in tail dependence in equity portfolios," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 351-368.
    5. 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.
    6. Juwon Seo, 2018. "Randomization Tests for Equality in Dependence Structure," Papers 1811.02105,
    7. Gautier Marti & S'ebastien Andler & Frank Nielsen & Philippe Donnat, 2016. "Clustering Financial Time Series: How Long is Enough?," Papers 1603.04017,, revised Apr 2016.
    8. 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.
    9. Jiang, Chun-Fu & Peng, Hong-Yi & Yang, Yu-Kuan, 2016. "Tail variance of portfolio under generalized Laplace distribution," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 187-203.
    10. 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.
    11. Gautier Marti & Sébastien Andler & Frank Nielsen & Philippe Donnat, 2016. "Clustering Financial Time Series: How Long is Enough?," Post-Print hal-01400395, HAL.
    12. Michael R. Metel & Traian A. Pirvu & Julian Wong, 2017. "Risk Management under Omega Measure," Risks, MDPI, Open Access Journal, vol. 5(2), pages 1-14, May.
    13. Chao Gong & Chunhui Xu & Ji Wang, 2018. "An Efficient Adaptive Real Coded Genetic Algorithm to Solve the Portfolio Choice Problem Under Cumulative Prospect Theory," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 227-252, June.
    14. Tiago P. Filomena & Miguel A. Lejeune, 2014. "Warm-Start Heuristic for Stochastic Portfolio Optimization with Fixed and Proportional Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 308-329, April.
    15. Kangrong Tan & Meifen Chu, 2012. "Estimation Of Portfolio Return And Value At Risk Using A Class Of Gaussian Mixture Distributions," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 6(1), pages 97-107.
    16. Paolella, Marc S. & Polak, Paweł & Walker, Patrick S., 2019. "Regime switching dynamic correlations for asymmetric and fat-tailed conditional returns," Journal of Econometrics, Elsevier, vol. 213(2), pages 493-515.
    17. 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.
    18. 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.
    19. González-Pedraz, Carlos & Moreno, Manuel & Peña, Juan Ignacio, 2014. "Tail risk in energy portfolios," Energy Economics, Elsevier, vol. 46(C), pages 422-434.


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