Analyzing most of world financial crises showed that, illiquid assets were the most important factor in the occurrence of these crises. So, it's necessary for investment institutes to consider liquidity risks in addition to calculate returns volatility risk in their long term investment strategies to gain the highest revenue. This research is going to suggest the optimum portfolio of Tehran Stock Exchange industries with focus in relationship between these industries and their bid-ask spread by VAR-Multivariate GARCH and Value at Risk approach. For this purpose, optimum portfolio of these industries was comprised in two cases-considering liquidity risk and regardless of this risk. Results showed that, Multidisciplinary industrial, Communication and Bank industries had the most quotas in portfolio, when we didn't consider liquidity risk. However Automobile industry will replace Bank industry if we consider liquidity risk parameters.

A matrix A is said to be Multivariate majorized by a matrix B, written A ≺ B, if there exists a doubly stochastic matrix D such that A = BD. In the present paper, we obtain a totally ordered subset of Mnm which contains a given matrix A. Also, we show that the totality of all extreme points of the collection of all matrices which are Multivariately majorized by a matrix A is the set of all matrices obtained by permuting the columns of A.