基于因素模型的协高阶矩矩阵估计及其应用研究

Research on Higher-order Comoment Matrix Estimation Based on a Factor Model and Its Application

在高阶矩投资组合中,使用传统样本估计方法会产生较高估计误差和模型设定误差。本文在多因素模型的基础上,给出一种改进的协高阶矩估计方法,分析了基于多因素模型压缩估计量的渐进一致性。蒙特卡洛模拟表明,多因素压缩估计量在有限样本中具有更小的平均绝对误差、根均方误差以及更高的平均绝对改进百分比,有效提高了协高阶矩矩阵估计的精度;即使在样本观测量比资产数目少时,估计的协高阶矩矩阵精度都会有较大提高。基于2005年6月至2019年5月沪深300成分股的高阶矩投资组合实证发现,多因素压缩方法与其他估计方法相比,在年化收益率上可以获得4.7%~32.8%的提升,最大回撤能够下降3.7%~18.3%,表明使用多因素压缩估计方法构建的投资组合有更大的可能获得更多货币效用增益,以及面临亏损时,产生的最大亏损更小。该方法有助于金融机构或理性投资者在进行投资组合时减小投资损失,获得更好的投资回报。

In the higher-order moment portfolio,the traditional estimation method will have larger estimation error and model setting error.Based on the multi-factor model,this paper gives an improved estimation method for higher-order comoment matrices and the asymptotic consistency of the shrinkage estimators.The Monte Carlo simulation shows that the multi-factor shrinkage estimator has smaller average absolute error,root mean square error,and a higher percentage improvement in average absolute error in a finite sample.It effectively improves the accuracy of the higher-order comoment matrix estimation,even when the sample observation is smaller than the number of assets.Based on the empirical evidence of higher-order moment portfolios of CSI 300 stocks from June 2005 to May 2019,compared with other estimation methods,the multi-factor shrinkage method can improve 4.7%~32.8%in annualized return and the maximum drawdown can fall by 3.7%~18.3%.It indicates that the investment portfolio constructed by the multi-factor shrinkage estimation method has a higher possibility to obtain a greater monetary utility gain,and the maximum loss,if in a loss,is smaller.This method helps financial institutions or rational investors to reduce investment losses and obtain better investment returns when investing in portfolios.