证券数目变化时受到扰动的M-V有效前沿分析

The Analysis of the M-V Efficient Frontier with Perturbation as the Security Number Changes

基于M-V证券组合模型,在证券市场上不存在无风险资产且允许卖空条件下,探讨了证券数增加k种后原n种证券协方差矩阵发生改变情形下M-V证券组合有效前沿的漂移问题。通过引入扰动因子和扰动矩阵,给出了M-V证券组合有效前沿的漂移方向及其开口大小的变化情况．研究结果表明证券数增加了k种后有效前沿向左漂移以及它的开口变大,原证券组合的有效前沿完全落在新的证券组合可行集内．

Based on M-V portfolio model, the drift of M-V portfolio efficient frontier on condition that there isn＇t exist risk-less security and short sales are allowed in the market is studied when the number of securities increases and the covariance matrix of former n securities changes. The drift direction and the change of opening of M-V portfolio efficient frontier are given by means of perturbation factor and perturbation matrix. The results show that the new efficient frontier drift to right and its opening is more broad to the old one, and also the old portfolio opportunity set is a subset of the new one.