Mean-Variance Portfolio Selection With 'At-Risk' Constraints and Discrete Distributions

Posted: 1 Apr 2007 Last revised: 5 Sep 2008

See all articles by Gordon J. Alexander

Gordon J. Alexander

University of Minnesota - Twin Cities - Carlson School of Management

Alexandre M. Baptista

George Washington University - School of Business

Shu Yan

Oklahoma State University - Stillwater - Department of Finance

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.

Keywords: Value-at-risk, Conditional value-at-risk, Portfolio selection, Discrete distributions

JEL Classification: G11, D81

Suggested Citation

Alexander, Gordon J. and Baptista, Alexandre M. and Yan, Shu, Mean-Variance Portfolio Selection With 'At-Risk' Constraints and Discrete Distributions. Journal of Banking and Finance, Vol. 31, No. 12, pp. 3761-3781, December 2007, Available at SSRN: https://ssrn.com/abstract=976450

Gordon J. Alexander (Contact Author)

University of Minnesota - Twin Cities - Carlson School of Management ( email )

19th Avenue South
Minneapolis, MN 55455
United States
612-624-8598 (Phone)
612-624-1335 (Fax)

Alexandre M. Baptista

George Washington University - School of Business ( email )

School of Business, Funger Hall, Suite 501
2201 G Street, NW
Washington, DC 20052
United States
202-994-3309 (Phone)
202-994-5014 (Fax)

HOME PAGE: http://home.gwu.edu/~alexbapt/

Shu Yan

Oklahoma State University - Stillwater - Department of Finance ( email )

Spears School of Business
Stillwater, OK 74078-4011
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Abstract Views
725
PlumX Metrics