The paper studies the po rtfo lio op t im izat ion p rob lem under V aR m easu re w here the dist ribu t ion s of retu rn s are of fat tails. It has p roved that the op t im al po rtfo lio based on the second o rder fat tails converges to the op t im al po rtfo lio based on the f irst o rder fat tails. The resu lt show s that it need on ly con st ruct the op t im al po rtfo lio based on the f irst o rder fat tails w h ich is enough to guaran tee a good app rox im at ing accu racy w hen the requ ired risk level is suff icien t low. Thu s the comp lex compu tat ion fo r the po rtfo lio op t im izat ion w ith h igher o rder fat tails can be avo ided.