Portfolio optimization problems with linear programming models

In this paper, we discuss four models proposed by Konno, Cai, Teo and Markowitz respectively. Two groups of data (one from 33 securities over 72 months, the other from 63 securities over 120 months) are used to examine these models. Efficient frontiers are presented. The utility levels in the four models do not decrease at the same rate with the change of the risk-aversion factor. Cai’s model provides the highest utility value and Markowitz’s provides the lowest one in most cases. When the expected returns are confronted with the true ones at the end of a 10-month period, Markowitz’s and Konno’s models seem to have similar tendencies while Cai’s and Teo’s models seem to have similar tendencies, and the four models get higher true wealth compared with Nikkei 225 and Nikkei 500 index respectively in most cases.