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Portfolio selection based on the mean-VaR efficient frontier

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  • Chueh-Yung Tsao

Abstract

Value-at-Risk (VaR) has become one of the standard measures for assessing risk not only in the financial industry but also for asset allocations of individual investors. The traditional mean-variance framework for portfolio selection should, however, be revised when the investor's concern is the VaR instead of the standard deviation. This is especially true when asset returns are not normal. In this paper, we incorporate VaR in portfolio selection, and we propose a mean-VaR efficient frontier. Due to the two-objective optimization problem that is associated with the mean-VaR framework, an evolutionary multi-objective approach is required to construct the mean-VaR efficient frontier. Specifically, we consider the elitist non-dominated sorting Genetic Algorithm (NSGA-II). From our empirical analysis, we conclude that the risk-averse investor might inefficiently allocate his/her wealth if his/her decision is based on the mean-variance framework.

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  • Chueh-Yung Tsao, 2010. "Portfolio selection based on the mean-VaR efficient frontier," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 931-945.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:8:p:931-945
    DOI: 10.1080/14697681003652514
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    Cited by:

    1. Huang, Xiaoxia & Zhao, Tianyi, 2014. "Mean-chance model for portfolio selection based on uncertain measure," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 243-250.
    2. Ji Cao, 2017. "How does the underlying affect the risk-return profiles of structured products?," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 31(1), pages 27-47, February.
    3. Fernando Vega-Gámez & Pablo J. Alonso-González, 2024. "How likely is it to beat the target at different investment horizons: an approach using compositional data in strategic portfolios," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-17, December.
    4. 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.
    5. Ravi Kashyap, 2024. "The Blockchain Risk Parity Line: Moving From The Efficient Frontier To The Final Frontier Of Investments," Papers 2407.09536, arXiv.org.
    6. Víctor M. Adame-García & Fernando Fernández-Rodríguez & Simón Sosvilla-Rivero, "undated". "Portfolios in the Ibex 35 index: Alternative methods to the traditional framework, a comparative with the naive diversification in a pre- and post- crisis context," Documentos de Trabajo del ICAE 2015-07, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised Jun 2015.
    7. Víctor Adame-García & Fernando Fernández-Rodríguez & Simón Sosvilla-Rivero, 2017. "“Resolution of optimization problems and construction of efficient portfolios: An application to the Euro Stoxx 50 index"," IREA Working Papers 201702, University of Barcelona, Research Institute of Applied Economics, revised Feb 2017.

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