TheVaR,anewappearingfinancialrisk-managetool,havebeenappliedwidely.ManyfinancialsetupshaveaccustomedtomeasuretheriskofaportfoliowiththeVaR.SoitisverynecessarytodiscusstheportfoliochoiceproblemundertheVaRconstraint.Inthispaper,bysettingandsolvingtheportfoliochoicemodelundertheVaRconstraint,weillustratethattheuseoftheVaRconstraintreducesthearrayofchoicetoamoremanageablerange.TheprobabilityoftragetVaR,therefore,canbethoughtofasarisktoleranceassessmenttool(whencoupledwithanothermeasureofrisk).