DP2997 Mean Variance Portfolio Allocation with a Value at Risk Constraint

Author(s): Enrique Sentana
Publication Date: October 2001
Keyword(s): market risk capital, portfolio frontier, risk management
JEL(s): G11
Programme Areas: Financial Economics
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=2997

In this Paper, I first provide a simple unifying approach to static Mean-Variance analysis and Value at Risk, which highlights their similarities and differences. Then I use it to explain how fund managers can take investment decisions that satisfy the VaR restrictions imposed on them by regulators, within the well-known Mean-Variance allocation framework. I do so by introducing a new type of line to the usual mean-standard deviation diagram, called IsoVaR,which represents all the portfolios that share the same VaR for a fixed probability level. Finally, I analyse the 'shadow cost' of a VaR constraint.