均值方差模型改进及实证检验
Improvement and Empirical Testing of Mean Variance Model

如何能够在投资中有效地降低风险并获得可观收益，一直是投资者关注的问题。本文根据Markowitz经典的投资组合理论，对均值–方差模型、均值–下半方差模型和组合偏差模型进行了介绍，利用上证50成分股2021年数据求解投资组合，2022年数据进行回测并比较上述模型与等比例投资的表现。结果显示：1) 从投资组合的表现来看，组合偏差 > 均值–下半方差 > 均值–方差 > 等比例投资；2) 衡量投资组合的风险时应当将超额收益的因素考虑进去；3) 衡量投资组合风险时下半方差是主要的因素。
How to effectively reduce risks and achieve considerable returns in investment has always been a concern for investors. This article introduces the mean variance model, mean lower half variance model, and portfolio bias model based on Markowitz’s classic portfolio theory. The investment portfolio is solved using the 2021 data of the Shanghai Stock Exchange’s 50 component stocks, and the 2022 data is backtested to compare the performance of the above models with proportional investments. The results show that: 1) From the performance of the investment portfolio, portfolio bias > mean lower half variance > mean variance > proportional investment; 2) When measuring the risk of an investment portfolio, the factor of excess returns should be taken into account; 3) The lower half variance is the main factor in measuring portfolio risk.