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.

在本文中，我们分别讨论了由康诺（Konno）、蔡（Cai）、张智强（Teo）和马科维茨（Markowitz）提出的四种模型。使用了两组数据（一组是72个月内的33种证券，另一组是120个月内的63种证券）来检验这些模型。给出了有效前沿。随着风险厌恶系数的变化，这四种模型中的效用水平并非以相同的速率下降。在大多数情况下，蔡的模型提供的效用值最高，而马科维茨的模型提供的效用值最低。当预期收益在10个月期末与实际收益相对比时，马科维茨和康诺的模型似乎有相似的趋势，蔡和张智强的模型似乎也有相似的趋势，并且在大多数情况下，这四种模型相较于日经225指数和日经500指数分别获得了更高的实际财富。