Stochastic dominance and risk measure: A decision-theoretic foundation for VaR and C-VaR

Chenghu Ma, Wing Keung WONG*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)

Abstract

Is it possible to obtain an objective and quantifiable measure of risk backed up by choices made by some specific groups of rational investors? To answer this question, in this paper we establish some behavior foundations for various types of VaR models, including VaR and conditional-VaR, as measures of downside risk. In this paper, we will establish some logical connections among VaRs, conditional-VaR, stochastic dominance, and utility maximization. Though supported to some extents with unanimous choices by some specific groups of expected or non-expected-utility investors, VaRs as profiles of risk measures at various levels of risk tolerance are not quantifiable - they can only provide partial and incomplete risk assessments for risky prospects. We also include in our discussion the relevant VaRs and several alternative risk measures for investors; these alternatives use somewhat weaker assumptions about risk-averse behavior by incorporating a mean-preserving-spread. For this latter group of investors, we provide arguments for and against the standard deviation versus VaR and conditional-VaRs as objective and quantifiable measures of risk in the context of portfolio choice.

Original languageEnglish
Pages (from-to)927-935
Number of pages9
JournalEuropean Journal of Operational Research
Volume207
Issue number2
DOIs
Publication statusPublished - 1 Dec 2010

Scopus Subject Areas

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

User-Defined Keywords

  • Decision analysis
  • Risk analysis
  • Risk attributes
  • Stochastic dominance
  • Utility

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