统计因子、经济因子,殊途同归?  

Can statistical factors and economic factors reach the same goal in different ways?

作　　者：倪宣明 郑田田 孙会霞 赵慧敏[3] NI Xuanming;ZHENG Tiantian;SUN Huixia;ZHAO Huimin(School of Software and Microelectronics,Peking University,Beijing 100871,China;School of Public Finance and Tax,Central University of Finance and Economics,Beijing 100081,China;School of Business,Sun Yat-sen University,Guangzhou 510275,China)

机构地区：[1]北京大学软件与微电子学院,北京100871 [2]中央财经大学财政税务学院,北京100081 [3]中山大学管理学院,广州510275

出　　处：《系统工程理论与实践》2023年第12期3385-3406,共22页Systems Engineering-Theory & Practice

基　　金：广东省自然科学基金(2022A1515011893);国家自然科学基金(71991474,71973147)。

摘　　要：套利定价理论认为理想的风险因子需要能够同时对资产期望收益率(一阶矩)和方差-协方差矩阵(二阶矩)定价,因此在构造风险因子的过程中,将收益率截面的一、二阶矩信息联系起来至关重要.基于资产定价和投资组合理论,本文认为夏普率是联系一、二阶矩的理想指标,并基于该指标提出了一种均值方差有效的稀疏主成分分析算法,构造潜在风险因子,该算法在主成分分析(principal component analysis, PCA)的基础上引入了夏普率信息,即通过在PCA的目标函数中引入L1正则项对原主成分进行稀疏调整,并以最大化夏普率的原则来确定惩罚项系数.经过这一过程,由本文算法提取的因子可在捕捉股票市场共同运动的同时也能实现对截面资产期望收益率差异的定价.且进一步解析发现,本文所构造因子的权重结构与经典经济因子的权重结构类似,这说明本文所提的统计因子本质上与经济因子的金融逻辑是一致的.本文利用A股市场2002年4月至2022年5月的月频数据,基于A股市场上常见的18个异象特征依次构造5×5和10×10交叉排序组合数据集、异象特征单排序组合数据集来检验本文算法的定价能力.结果显示,由本文算法构造的因子模型的定价能力优于传统三因子、四因子、五因子模型,并且也优于PCA、风险溢价PCA这类统计因子模型,表现为测试资产的GRS统计量更小,并且由本文算法提取的因子可以实现更大的最优夏普率.进一步发现,虽然经本文算法提取的因子属于统计因子,但其同样具有较明显的经济学含义,其中基于5×5交叉排序组合提取的前三个主成分的权重分布可分别还原经济因子模型中的市场因子、规模因子、价值因子.以上结论在10×10交叉排序组合数据集和更为一般的异象特征单排序组合数据集中同样成立,表明本文结论具有一定的稳健性.According to the arbitrage asset pricing(APT)theory,an ideal risk factor needs to be able to price both the expected return(first-order moment)and variance-covariance matrix(second-order moment)of the cross-sectional assets.Therefore,it is very important to link the order moment information in the process of building risk factors.Based on the asset pricing and portfolio optimization theory,this paper considers the Sharpe ratio to be an ideal indicator for linking the first and second moments,and proposes a sparse principal component analysis algorithm with mean-variance efficiency(MVE-SPCA)to build risk factors.Specifically,the algorithm introduces Sharpe ratio information on the basis of principal component analysis(PCA),that is,the original principal component is sparsely adjusted by introducing the L1 regularization term into the objective function of PCA,and the coefficient of the penalty term is determined by maximizing the Sharp ratio.Through this process,factors can not only capture the co-movement of the stock market,but also price the differences in the expected returns of cross-sectional assets.Further analysis shows that the weight structure of the factors constructed in this paper is similar to that of the classical economic factors,which shows that the statistical factors proposed in this paper are essentially consistent with the financial logic of the classical economic factors.Using the monthly frequency data of the A-share market from April 2002 to May 2022,this paper constructs 5×5 and 10×10 cross-sorted portfolio data sets and single-sorted portfolio data sets based on the common 18 anomalies in the A-share market to test the pricing ability of the proposed algorithm.The results show that the pricing ability of the factor model constructed by the algorithm in this paper is better than the traditional three-factor,four-factor and five-factor models,and also better than the statistical factor models such as PCA and risk premium PCA.The factor model built by the algorithm in this paper has smalle

关 键 词：资产定价 潜在风险因子 主成分分析 投资组合优化 

分 类 号：F830.9[经济管理—金融学]