基于收益权重的均值-熵投资组合模型的研究

The Mean-Entropy Model for Portfolio Optimization Selection Based on Return Weight

在经典的均值-方差模型中,研究者往往假设收益率服从正态分布,用收益率均值估计其期望。但在实际问题中收益率往往不满足假设,同时考虑到方差度量风险的局限性,从而我们构建均值-熵模型,其中收益率期望用每个时间段收益占总时间段收益权重(θt)来计算。本文通过对深圳A股进行筛选,并从中选取5只股票进行实证分析,然后讨论了θt的合理性;熵方法和方差法的一致性;不含无风险证券和含无风险证券均值-熵投资组合模型的比较分析等问题。结果表明:引入θt计算收益率期望时,均值-方差模型的有效边界仍是一条较好的抛物线;熵方法和方差法具有一致性;且在相等收益水平下,熵方法能够更好的分散投资风险。

In the traditional mean-variance model,researchers tend to assume that return rate obeys normal distribution which is always not satisfied with most questions,and estimate expectation value with its average,simultaneously considering the limitations of variance.So,the mean-entropy model based on return weight has been proposed.In this paper,we choose five A-stocks in application.Then,we study the rationality of θt,present the consistency of the entropy method and variance method,and do some research on comparison between no riskfree securities and risk-free securities.The results show that computing the expectation of return rate based onθt,the efficient frontier of mean-variance model is still a good parabola,the consistency of entropy method and variance method is proved,and entropy method can better disperse the risk when return rate is equal.