基于BP神经网络的三因子均值-方差投资组合优化  

Portfolio Optimization of Three Factor Mean-Variance Model Based on BP Neural

作　　者：张鹏 朱岁虹 崔淑琳 ZHANG Peng;ZHU Sui-hong;CUI Shu-lin(School of Economics Management,South China Normal University,Guangzhou 510006,China)

机构地区：[1]华南师范大学经济与管理学院,广东广州510006

出　　处：《数学的实践与认识》2025年第1期26-40,共15页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71271161);广东省自然科学基金项目(2024A1515011808);广东省教育厅项目(2023ZDZX4131);广东省教育科学规划课题(2024GXJK032)。

摘　　要：基于资产的历史收益率信息,运用最小二乘法拟合Fama-French三因子模型中资产收益率与市场因子、规模因子和账面市值因子等公共因子之间的关系.在此基础上使用BP神经网络预测公共因子,进而计算资产的预期收益.考虑V型交易成本,借贷限制和阈值约束,构建了基于BP神经网络的三因子均值-方差投资组合模型(FFMV).该模型是是一个凸二次规划问题,运用不等式组的旋转算法进行求解.最后,从沪深A股中随机选取48支股票为样本进行实证分析.样本内分析发现:当其他条件相同时,交易成本越高,投资组合有效前沿水平越低;风险资产交易量上界越高、无风险资产的可借入量越高,投资组合有效前沿水平越高.样本外检验表明:相较于等比例投资组合模型和上海证券综合指数,基于BP神经网络的三因子均值-方差投资组合模型的累计收益率、年度夏普比率和年度索提诺比率水平更高.Based on the historical asset return,this paper uses the ordinary least square(OLS)method to fit the model between return and common factors,ie.market factors,firm size factors,and book-to-market equity,in the Fama-French model.On this basis,the BP neural network is used to predict common factors,and then calculate the asset's expected returns.Considering V-shaped transaction costs,borrowing and lending restrictions,and threshold constraints,this paper constructs a three-factor mean-variance investment portfolio model(FFMV)based on the BP neural network.The model is a convex quadratic programming problem and can be solved by the pivoting algorithm of inequality systems.Finally,this article randomly selects 48 stocks from the Shanghai and Shenzhen A-shares as samples for empirical analysis.Through the in-sample analysis,it can be found that when other conditions are the same,the higher the transaction cost,the lower the effective frontier level of the portfolio;The higher upper bound on the trading volume of risky assets and the higher borrowing amount of risk-free assets,will both lead to the higher effective frontier level of the portfolio.Out-of-sample analysis indicates that compared to the proportional investment portfolio model and the Shanghai Securities Composite Index,the three-factor mean-variance investment portfolio model based on the BP neural network has higher levels of cumulative return,annual Sharpe ratio,and annual Sortino ratio.

关 键 词：投资组合 均值-方差模型 FAMA-FRENCH三因子模型 BP神经网络 旋转算法 

分 类 号：F832.51[经济管理—金融学] F224