Portfolio selection based on the mean-VaR efficient frontier

Chueh Yung Tsao*

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

14 Scopus citations


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.

Original languageEnglish
Pages (from-to)931-945
Number of pages15
JournalQuantitative Finance
Issue number8
StatePublished - 2010


  • Efficient frontiers
  • Genetic algorithms
  • Portfolio selection
  • Value at Risk


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