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Portfolio analysis with mean-CVaR and mean-CVaR-skewness criteria based on mean-variance mixture models

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Listed:
  • Nuerxiati Abudurexiti
  • Kai He
  • Dongdong Hu
  • Svetlozar T. Rachev
  • Hasanjan Sayit
  • Ruoyu Sun

Abstract

The paper Zhao et al. (2015) shows that mean-CVaR-skewness portfolio optimization problems based on asymetric Laplace (AL) distributions can be transformed into quadratic optimization problems under which closed form solutions can be found. In this note, we show that such result also holds for mean-risk-skewness portfolio optimization problems when the underlying distribution is a larger class of normal mean-variance mixture (NMVM) models than the class of AL distributions. We then study the value at risk (VaR) and conditional value at risk (CVaR) risk measures on portfolios of returns with NMVM distributions. They have closed form expressions for portfolios of normal and more generally elliptically distributed returns as discussed in Rockafellar & Uryasev (2000) and in Landsman & Valdez (2003). When the returns have general NMVM distributions, these risk measures do not give closed form expressions. In this note, we give approximate closed form expressions for VaR and CVaR of portfolios of returns with NMVM distributions. Numerical tests show that our closed form formulas give accurate values for VaR and CVaR and shortens the computational time for portfolio optimization problems associated with VaR and CVaR considerably.

Suggested Citation

  • Nuerxiati Abudurexiti & Kai He & Dongdong Hu & Svetlozar T. Rachev & Hasanjan Sayit & Ruoyu Sun, 2021. "Portfolio analysis with mean-CVaR and mean-CVaR-skewness criteria based on mean-variance mixture models," Papers 2111.04311, arXiv.org, revised Feb 2023.
  • Handle: RePEc:arx:papers:2111.04311
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    References listed on IDEAS

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    3. Shangmei Zhao & Qing Lu & Liyan Han & Yong Liu & Fei Hu, 2015. "A mean-CVaR-skewness portfolio optimization model based on asymmetric Laplace distribution," Annals of Operations Research, Springer, vol. 226(1), pages 727-739, March.
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    Cited by:

    1. 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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