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Portfolio optimization under a generalized hyperbolic skewed t distribution and exponential utility

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  • John R. Birge
  • Luis Chavez-Bedoya

Abstract

In this paper, we show that if asset returns follow a generalized hyperbolic skewed t distribution, the investor has an exponential utility function and a riskless asset is available, the optimal portfolio weights can be found either in closed form or using a successive approximation scheme. We also derive lower bounds for the certainty equivalent return generated by the optimal portfolios. Finally, we present a study of the performance of mean--variance analysis and Taylor’s series expected utility expansion (up to the fourth moment) to compute optimal portfolios in this framework.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:7:p:1019-1036
    DOI: 10.1080/14697688.2015.1113307
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    Cited by:

    1. Valeria V. Lakshina, 2019. "Do Portfolio Investors Need To Consider The Asymmetry Of Returns On The Russian Stock Market?," HSE Working papers WP BRP 75/FE/2019, National Research University Higher School of Economics.
    2. Nicholas Barberis & Lawrence J. Jin & Baolian Wang, 2021. "Prospect Theory and Stock Market Anomalies," Journal of Finance, American Finance Association, vol. 76(5), pages 2639-2687, October.
    3. Lakshina, Valeriya, 2020. "Do portfolio investors need to consider the asymmetry of returns on the Russian stock market?," The Journal of Economic Asymmetries, Elsevier, vol. 21(C).
    4. Wang, Chou-Wen & Liu, Kai & Li, Bin & Tan, Ken Seng, 2022. "Portfolio optimization under multivariate affine generalized hyperbolic distributions," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 49-66.
    5. Huang, Helen Hui & Sun, Jianchun & Zhang, Shunming, 2024. "Asset pricing for the lottery-like security under probability weighting: Based on generalized Wang transform," The North American Journal of Economics and Finance, Elsevier, vol. 71(C).
    6. Vanduffel, Steven & Yao, Jing, 2017. "A stein type lemma for the multivariate generalized hyperbolic distribution," European Journal of Operational Research, Elsevier, vol. 261(2), pages 606-612.
    7. Mikl'os R'asonyi & Hasanjan Sayit, 2022. "Exponential utility maximization in small/large financial markets," Papers 2208.06549, arXiv.org, revised Feb 2024.

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