不允许买空时的均值-下方风险投资组合选择——基于非参数估计方法

Mean-Downside Risk Portfolio Selection without Short Selling:Based on Nonparametric Estimation Methodology

本文分别利用下半方差和下半偏差度量下方风险(Downside Risk),采用非参数估计方法研究了不允许买空时的均值-下方风险投资组合选择问题。首先,我们利用组合收益率密度函数的非参数核(kernel)估计得到了下方风险的计算公式,并把它们嵌入到均值-下方风险投资决策模型中。然后得到了模型最优解存在的充要条件,并给出了求解最优投资策略的Zoutendijk可行方向算法。最后,基于中国股票市场真实数据给出了一个数值算例,并比较了在两种不同下方风险度量下模型的差别。

This paper adopts the methodology of nonparametric estimation to explore a mean-downside risk portfolio selection problem, where the downside risk is measured by semi-variance and semi-absolute deviation, respectively. First, we obtain the nonparametric estimated calculation formulas for downside risk by using the nonparametric estimation of the portfolio return＇s density function, and embed them into the mean-downside risk models. Then, we obtain a necessary and sufficient existence condition for optimal solution to the models, and give the Zoutendijk feasible direction algorithm for solving the optimal investment strategy of the models. Finally a numerical example based on real data of Chinese stock market is provided, and the two models in different downside risk measures are compared.