基于参数法的效用最大化投资组合有效前沿研究

摘要

针对不允许卖空的情况,分别提出不合有无风险资产(即仅含有风险资产)和含有无风险资产两种情况的效用最大化投资组合模型,并运用不等式组旋转算法的参数法研究两模型有效前沿的结构特征.结果表明,当仅含有风险资产时,投资组合的有效前沿是一条连续但不一定光滑的分段抛物线;当含有无风险资产,且风险资产是不允卖空的而无风险资产是允许卖空的时,投资组合有效前沿是一条连续的射线.两种情况的风险偏好系数均只在某个区间能较好地反映投资者对期望收益率和风险的权衡.此外,还验证了不等式组的旋转算法具有操作简便且计算效率高等优点.%The paper proposes two portfolio selection models with risk assets or with risk-free assets maximizing the utility without short sales and uses a parameter method based on the pivoting algorithm to study the efficient frontier. The result indicates that the efficient frontier of the model with risk assets only is continuous but not always derivative parabolas, but the efficient frontier of the model with risk-free asset permitting short sales and with risk assets not permitting short sales is a continuous line. The risk preference coefficients only reflect the investor's trade-off between the expected rate of return and risk within some intervals. The algorithm is proved to be efficient and easy to operate.