基本指数-最小下半方差投资组合优化研究

The Mixture of Fundamental Indexing and Minimum Semi-variance Portfolio Selection

为了克服方差作为风险度量无法区分收益和损失的局限性,同时弥补经典均值-方差模型忽略了企业基本面状况的缺陷,该文结合下半方差和基本指数的优点,分别考虑1-、2-范数交易成本,构建了基于期望效用最大化的基本指数-最小下半方差投资组合模型(简称“FI-semiv模型”),并运用不等式组的旋转算法进行求解.文章通过“滚动窗口”的方法,对FI-semiv模型进行了样本外检验与分析,并进一步将该模型与最小方差模型、最小下半方差模型和等比例投资模型的夏普比率进行对比.结果表明:基于FI-semiv模型构建的投资组合的夏普比率得到了有效提高,FI-semiv投资组合的风险更小,投资效率更高.

In order to overcome the limitation of variance in distinguishing income and loss and solve the problem caused by ignoring the fundamentals in MV model,a mixture of Fundamental Indexing and minimum semi-variance portfolio(“FI-semiv”model),taking into consideration 1-and 2-norm transaction costs respectively and aiming to maximize the expected utility of investors,is proposed and solved with the pivoting algorithm.The model is a convex quadratic programming problem with linear equality and inequality constraints.Based on the“rolling sample”approach,the out-of-sample sharp ratios of different models are compared.It turns out that the sharp ratio of the FI-semiv portfolio has been effectively improved,which means that the portfolio is less risky and more efficient.