TY - JOUR

T1 - Mean-variance portfolio selection with 'at-risk' constraints and discrete distributions

AU - Alexander, Gordon J.

AU - Baptista, Alexandre M.

AU - Yan, Shu

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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.

AB - 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.

KW - Conditional value-at-risk

KW - Discrete distributions

KW - Portfolio selection

KW - Value-at-risk

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U2 - 10.1016/j.jbankfin.2007.01.019

DO - 10.1016/j.jbankfin.2007.01.019

M3 - Article

AN - SCOPUS:36048938488

VL - 31

SP - 3761

EP - 3781

JO - Journal of Banking and Finance

JF - Journal of Banking and Finance

SN - 0378-4266

IS - 12

ER -