Mean-Variance Portfolio Allocation with a Value at Risk Constraint

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Abstract
In this paper, I first provide a unifying approach to 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 within the well-known Mean-Variance allocation framework that satisfy the VaR restrictions imposed on them by regulators. 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.

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