Mean-variance portfolio selection with 'at-risk' constraints and discrete distributions

Gordon J. Alexander, Alexandre M. Baptista, Shu Yan

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

We examine the impact of adding either a VaR or a CVaR constraint to the mean-variance model when security returns are assumed to have a discrete distribution with finitely many jump points. Three main results are obtained. First, portfolios on the VaR-constrained boundary exhibit (K + 2)-fund separation, where K is the number of states for which the portfolios suffer losses equal to the VaR bound. Second, portfolios on the CVaR-constrained boundary exhibit (K + 3)-fund separation, where K is the number of states for which the portfolios suffer losses equal to their VaRs. Third, an example illustrates that while the VaR of the CVaR-constrained optimal portfolio is close to that of the VaR-constrained optimal portfolio, the CVaR of the former is notably smaller than that of the latter. This result suggests that a CVaR constraint is more effective than a VaR constraint to curtail large losses in the mean-variance model.

Original languageEnglish (US)
Pages (from-to)3761-3781
Number of pages21
JournalJournal of Banking and Finance
Volume31
Issue number12
DOIs
StatePublished - Dec 1 2007

Keywords

  • Conditional value-at-risk
  • Discrete distributions
  • Portfolio selection
  • Value-at-risk

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