A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model
In this paper, we analyze the portfolio selection implications arising from imposing a value-at-risk (VaR) constraint on the mean-variance model, and compare them with those arising from the imposition of a conditional value-at-risk (CVaR) constraint. We show that for a given confidence level, a CVaR constraint is tighter than a VaR constraint if the CVaR and VaR bounds coincide. Consequently, a CVaR constraint is more effective than a VaR constraint as a tool to control slightly risk-averse agents, but in the absence of a risk-free security, has a perverse effect in that it is more likely to force highly risk-averse agents to select portfolios with larger standard deviations. However, when the CVaR bound is appropriately larger than the VaR bound or when a risk-free security is present, a CVaR constraint ÜdominatesÝ a VaR constraint as a risk management tool.
Volume (Year): 50 (2004)
Issue (Month): 9 (September)
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- Basak, Suleyman & Shapiro, Alexander, 2001.
"Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices,"
Review of Financial Studies,
Society for Financial Studies, vol. 14(2), pages 371-405.
- Suleyman Basak & Alex Shapiro, "undated". "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices," Rodney L. White Center for Financial Research Working Papers 6-99, Wharton School Rodney L. White Center for Financial Research.
- Suleyman Basak & Alexander Shapiro, 1999. "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-032, New York University, Leonard N. Stern School of Business-.
- Suleyman Basak & Alex Shapiro, "undated". "Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices," Rodney L. White Center for Financial Research Working Papers 06-99, Wharton School Rodney L. White Center for Financial Research.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(04), pages 1851-1872, September.
- Ralph C. Kimball, 2000. "Failures in risk management," New England Economic Review, Federal Reserve Bank of Boston, issue Jan, pages 3-12.
- Susanne Emmer & Claudia Klüppelberg & Ralf Korn, 2001. "Optimal Portfolios with Bounded Capital at Risk," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 365-384.
- Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July. Full references (including those not matched with items on IDEAS)
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