M arkow itz’ smean2variancemodel describes the risk of asset by variance, but variancemay not exist because of fat2tailedness of asset returns. A s ameasure of risk, mean absolute deviation is better than variance in a sense. In th is paper, a portfolio choice model is p roposed based on mean absolute deviation. The solution of the model is obtained by a simulated annealing algorithm. In order to compare the new modelsw ithM arkow itz one, a risk elasticity is defined. The emp irical result show s that the absolute values of risk elasticity are more than 1 under various returns and it also indicates that the p roposed model based on mean absolute deviation is better than mean2variance model based on variance both in theory and in p ractice. Two2fund separation is found in mean absolute deviation portfolio choice model