基于加权主成分分析的投资组合优化  

Portfolio Optimization Based on Weighted Principal Component Analysis

作　　者：孙会霞 SUN Huixia(School of Public Finance and Tax,Central University of Finance and Economics,Beijing 100081)

机构地区：[1]中央财经大学财政税务学院,北京100081

出　　处：《系统科学与数学》2023年第7期1888-1903,共16页Journal of Systems Science and Mathematical Sciences

摘　　要：金融资产收益率满足因子模型已成为实证资产定价领域的共识,因此在面临均值-方差(mean-variance,MV)投资组合优化问题时,基于因子模型构建期望收益率和方差-协方差矩阵估计量具有更好的经济学理论支撑,从而有助于提高输入参数的估计精度,改进MV策略的绩效表现.基于这一考虑,文章提出了一种可同时兼顾期望收益率和方差-协方差矩阵估计误差的加权主成分分析(weighted principal component analysis,WPCA)算法,该算法在经典主成分分析的目标函数中引入了收益率一阶矩估计误差的加权项,从而克服了经典主成分分析提取的因子在解释收益率一阶矩时的局限性.进一步文章基于WPCA算法提取的统计因子构建两个参数的估计量,然后将改进估计量带入MV策略中,得到WPCA-MV策略.实证上,文章基于A股市场199101-202209月5138只个股的月频收益率数据对WPCA-MV策略的样本外绩效表现进行评估,结果显示,与常见的投资组合策略MV,GMV,EW,BS,TZ等策略相比,文章所提的WPCA-MV策略在平均收益率,标准差,夏普率,累计收益率和换手率指标上均取得了优异的样本外表现,且这种优越性在美股75个因子数据集上同样成立,表明文章结论具有较好的稳健性.It has become common sense in the field of empirical asset pricing that the returns of financial assets satisfy the factor model form.Therefore,in the process of mean-variance(MV) portfolio optimization,estimators of the expected returns and the variance-covariance matrix based on the factor model have a more strong theoretical basis,thus will help improve the accuracy of the input parameters and further improve the performance of the MV strategy.Based on this consideration,this paper proposes an algorithm named weighted principal component analysis(WPCA)which takes into account the estimation error of both the expected returns and the variance-covariance matrix.This algorithm introduces a weighted term of the firstorder moment estimation error of the returns into the objective function of the classical principal component analysis,thus overcomes the limitation of the classical principal component analysis in explaining the first-order moment of the returns.Further,this paper constructs two parameter estimators based on the statistical factors extracted by the WPCA algorithm,and then applies the improved estimators to the MV strategy to obtain the WPCA-MV strategy.Empirically,this paper evaluates the out-of-sample performance of the WPCA-MV strategy based on monthly frequency return data of 5138 individual stocks in the A-share market from 199101 to 202209.The empirical results show that,compared with common strategies such as MV,GMV,EW,BS,TZ and so on,the WPCA-MV strategy proposed in this paper has excellent out-of-sample performances in terms of average return,standard deviation,Sharpe ratio,cumulative return and turnover.This superiority holds for the US data set consisting of 75 factor portfolios,indicating that the conclusions of this paper are robust.

关 键 词：投资组合优化 主成分分析 潜在因子模型 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] F831.51[自动化与计算机技术—控制科学与工程]