基于因子特征的高维稀疏投资组合优化

High-Dimensional Sparse Portfolio Optimization Based on Factor Characteristics

在高维情形下,为了实现对期望收益率的更准确估计,提高投资组合策略的稳定性及获得更好的样本外表现,文章利用流通市值和账面市值比的双因子排序组合信息,在回归形式的均值-方差策略目标函数中引入了Group-LASSO (GLASSO)正则项,构建了GLASSOMV投资组合策略.相比包含权重l_(1-)范数正则项的LASSO-MV策略,GLASSO-MV能够有效利用因子组合之间的定价差异信息,从而输出组间的稀疏权重,进而更有效地估计高维投资组合权重并取得更好的样本外表现.为了获得合适的正则项参数和权重稀疏度,文章在5折交叉验证寻优结果的基础上进行了稀疏度调整.为验证此策略,文章利用A股1995年至2019年共3695只股票的日际实证数据集,将GLASSO-MV与多种常见的投资组合策略进行了比较.结果显示相比LASSO-MV,MV,GMV,TZ (Tu-Zhou),BS (Bayes-Stein)等策略,GLASSO-MV实现了更好的样本外夏普率,更低的标准差风险和换手率.

When facing high-dimensional situation,to better estimate expected return,increase the stability of portfolio strategy and obtain better out-of-sample performance,this paper uses information of double-sorted portfolio on circulating market size and book-to-market to introduce a Group-LASSO(GLASSO) regularization term into the regression-type mean-variance objective function,and constructs the GLASSO-MV portfolio strategy.Comparing to l_(1-)norm regularized LASSO-MV strategy,GLASSO-MV can effectively utilitize the pricing difference among factor portfolios,and output sparse between-group weights,attaining more effective highdimensional weight estimation and better out-of-sample performance.To obtain suitable regularization term parameter and weight sparsity,this paper adopts 5-fold crossvalidation and adjusts the sparsity based on the parameter result.In terms of empirical study,this paper uses daily data on Chinese A share market from 1995 to 2019 of 3695 stocks,and compares GLASSO-MV to multiple common portfolio strategies.The result shows that,compared to strategies including LASSO-MV,MV,GMV,TZ(Tu-Zhou),BS(Bayes-Stein),GLASSO-MV has better out-of-sample Sharpe ratio,lower standard deviation risk and turnover.