结合“向后看”和“向前看”信息的投资组合优化  

Combining backward-looking information and forward-looking information in portfolio optimization

作　　者：黄羿 祝炜[3] 朱书尚 李端[4] HUANG Yi;ZHU Wei;ZHU Shushang;LI Duan(School of Business,Sun Yat-Sen University,Guangzhou 510275,China;School of Mathematics and Statistics,Jishou University,Jishou 416000,China;Huawei Technologies Co.Ltd,Shenzhen 518129,China;School of Data Science,City University of Hong Kong,Hong Kong 999077,China)

机构地区：[1]中山大学管理学院,广州510275 [2]吉首大学数学与统计学院,吉首416000 [3]华为技术有限公司,深圳518129 [4]香港城市大学数据科学学院,中国香港999077

出　　处：《系统工程理论与实践》2021年第4期861-881,共21页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(71471180,71721001,71571062)。

摘　　要：在均值-方差分析框架下,投资者需要估计收益率的均值向量和协方差矩阵等参数,最常用的方法是仅利用历史数据估计的"向后看"方法.然而,历史数据虽然能够提供经验参考,但并不能很好地预测未来.由于金融市场相对有效,市场表现本身包含了对预期的反应,但因为噪声交易者的存在,市场反应也必然夹杂着噪声.本文考虑知情交易者和噪声交易者的决策行为的异质性,并以此推导出市场均衡所隐含的关于预期收益率的信息结构.在此基础上,以"向后看"估计的均值向量分布为先验信息,以隐含均值向量预期且可观测的市场组合为新信息("向前看"信息),通过贝叶斯分析方法将两者有机结合得到均值向量的后验估计.理论分析表明知情交易者所占的市场份额越高、噪声交易强度越低或者知情交易者的风险厌恶程度越低,则"结合"方法将自适应地选择更多"向前看"信息进行预测,反之亦反.模拟实验和实证研究的结果进一步验证了相关理论分析的结论."结合"预测模型为投资组合管理提供了更加灵活、稳健的收益率预测方法.Under the framework of mean-variance analysis,investors need to estimate the mean vector and covariance matrix of asset returns to make investment decision.The most common estimation method is called"backward-looking"method since it relies only on historical data.However,it does not use the"forward-looking"information implied by the market variables,such as asset prices,and then cannot predict the future well.In this paper,we consider the general situation that market participants are consisting of informed investors and noise traders,and extract the"forward-looking"information on asset returns implied in the equilibrium market portfolio.By combining the historical"backward-looking"information with the market implied"forward-looking"information via Bayesian analysis,we propose a"combined"method for return prediction.The theoretical analysis show that the"combined"method can adaptively select more"forward-looking"information when the informed investor has a higher market share,a lower risk-averse degree,or the noise trader has a lower noise trading intensity;otherwise,it will use more"backward-looking"information.Both the simulation experiments and the empirical tests demonstrate that the"combined"model can provide more flexible and robust prediction on asset returns in portfolio management.

关 键 词：投资组合 贝叶斯分析 “向前看”信息 “向后看”信息 

分 类 号：F830.9[经济管理—金融学]