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Sharpe Ratio and Return-VaR Ratio Maximization for Option Portfolios with Skew-Elliptical $t$ Underlying Returns

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  • Kyle Sung
  • Traian A. Pirvu

Abstract

We provide a formulation for optimal option portfolios under Sharpe Ratio maximization when the underlying returns follow a skew-elliptical t-distribution. This departs from the traditional normal returns setting in the context of Sharpe ratio maximization by allowing the modelling of heavy-tailed and skewed dynamics. The novelty of this paper and our main result is to provide explicit formulas for the portfolio weights when maximizing the Sharpe ratio and return-to-Value-at-Risk (VaR) ratio in the skew-elliptical setting. Numerical experiments reveal that the optimal portfolios for the two ratios are different.

Suggested Citation

  • Kyle Sung & Traian A. Pirvu, 2026. "Sharpe Ratio and Return-VaR Ratio Maximization for Option Portfolios with Skew-Elliptical $t$ Underlying Returns," Papers 2606.17032, arXiv.org.
    • Handle: RePEc:arx:papers:2606.17032
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    References listed on IDEAS

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    1. Kyle Sung & Traian A. Pirvu, 2026. "Optimal Option Portfolios for Skew-Elliptical t Returns," Papers 2601.07991, arXiv.org, revised Apr 2026.
    2. 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.
    3. Farzad Pourbabaee & Minsuk Kwak & Traian A. Pirvu, 2016. "Risk minimization and portfolio diversification," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1325-1332, September.
    4. Yin, Chuancun & Balakrishnan, Narayanaswamy, 2024. "Stochastic representations and probabilistic characteristics of multivariate skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    5. Cui, Xueting & Zhu, Shushang & Sun, Xiaoling & Li, Duan, 2013. "Nonlinear portfolio selection using approximate parametric Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 37(6), pages 2124-2139.
    6. Kim, Hyoung-Moon & Mallick, Bani K., 2003. "Moments of random vectors with skew t distribution and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 417-423, July.
    7. Aditya Maheshwari & Traian A. Pirvu, 2020. "Portfolio Optimization under Correlation Constraint," Risks, MDPI, vol. 8(1), pages 1-18, February.
    8. Marc Genton & Nicola Loperfido, 2005. "Generalized skew-elliptical distributions and their quadratic forms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 389-401, June.
    9. Echaust Krzysztof, 2014. "A Comparison of Tail Behaviour of Stock Market Returns," Folia Oeconomica Stetinensia, Sciendo, vol. 14(1), pages 22-34, June.
    10. Wang, Kesen & Karling, Maicon J. & Arellano-Valle, Reinaldo B. & Genton, Marc G., 2024. "Multivariate unified skew-t distributions and their properties," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    11. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
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