Abstract: The existing multi-period portfolio diversification performance evaluation models are mainly divided into two categories. The first category is to build a performance evaluation model based on the return rate of portfolio at each period. The other category is to evaluate portfolio performance by using efficient frontier. However, the former ignores the dynamic relationship among the time periods, while the latter has limitations when there exists friction in financial market. To address this problem, the actual investment of the input-output process was clarified and defined, and the definition of multi-period portfolio efficiency were given based on the distance between portfolio under evaluation and its projection point on the efficient frontier. Under the multi-period mean-variance theoretical framework, the middle connection condition in the multi-period portfolio evaluation problem was derived by using the wealth dynamic process, so as to build a two-period portfolio efficiency estimation model under different orientation. Since the above-mentioned middle connection condition is random, it not workable in actual evaluation. Therefore, in this paper, the first moment and second moment of the above random conditions were used to replace the original one, and another kind of two-period portfolio efficiency estimation model was built. The numerical analyses show that this proposed model is effective.

Key words: multi-period portfolios, diversification model, performance evaluation, portfolio efficiency

摘要： 已有的多阶段分散化投资组合绩效评价模型主要分为两类：一类是基于各阶段收益率来构建评价模型；另外一类则是基于真实前沿面来评价投资组合绩效。前者忽略了投资组合在各阶段的动态联系，而后者则在市场存在摩擦时存在较大局限性。本文首先明确了实际投资的投入-产出过程，基于待评价投资组合与真实前沿面之间的距离，给出多阶段投资组合效率的定义。在多阶段均值-方差理论框架下，利用投资组合的财富动态过程，导出待评价投资组合在多阶段评价中所应满足的中间连接条件，从而构建不同导向下的两阶段分散化投资组合效率估计模型。由于上述中间连接条件为随机条件，这也导致它在实际评价中并不可取。本文以上述随机条件的一阶矩、二阶矩代替原有连接条件，从而构建一类确定型的两阶段分散化效率估计模型，并通过数值分析阐述了该类模型的有效性。

关键词: 多阶段投资组合, 分散化模型, 绩效评价, 投资组合效率