基于机器学习的多目标投资组合优化研究

Multi-objective Portfolio Selection Based on Machine Learning

文章首先运用随机森林、RBF神经网络和BP神经网络3种机器学习方法预测股票收盘价,使用历史数据和预测的收盘价计算投资组合的收益率均值、下半方差、偏度;然后,考虑交易成本、投资比例上下界约束和借贷约束,提出均值-下半方差-偏度多目标投资组合模型(M-SV-S)。该模型对应的优化问题属于非凸优化问题且求解困难,故首先将其转化为单目标优化模型,再运用差分进化算法进行求解。最后,选取上证50指数成分股作为样本进行实证分析,从收益率和索提诺比率等方面来对比M-SV-S模型与等比例投资组合模型的投资表现。实证结果表明:在样本外窗口内,M-SV-S模型的每日净收益率在1%~4%之间、30天的累计超额收益率超过50%、索提诺比率大于0,投资绩效明显优于等比例投资组合模型。

Firstly,random forest,RBF neural network and BP neural network are used to predict the closing price of stocks in this paper.Historical data and predicted closing prices are used to calculate the mean,downside semi-variance,and skewness of investment portfolio returns.Secondly,considering transaction costs,upper and lower bound,and borrowing and lending constraints,a multi-objective portfolio selection model(M-SV-S)based on machine learning is proposed.The optimization problem corresponding to this model belongs to non-convex optimization problems and is difficult to solve so that it is transformed into a single objective optimization model,which is solved by differential evolution algorithm.Finally,the component stocks of the SSE 50 Index is chosen as samples for empirical analysis.The investment performance of the M-SV-S is compared with the equal weight portfolio mo-del in terms of returns and Sortino ratio.The empirical results show that the daily net return of M-SV-S model between 1%and 4%,the cumulative abnormal return of 30 days of M-SV-S over 50%,and the Sortino ratio of M-SV-S greater than 0 within the out of sample window.It means that the investment performance of M-SV-S is significantly better than that of the equal weight portfolio model.