统计与数据科学学院知识库

伴着国民经济水平的提高，股票投资逐渐走进大众视野。众所周知股票投资具有很大的风险，尚待完善的监管体制、投资者从众心理以及恶意坐庄行为都会加大市场的风险。所以对于投资者来讲，最为关心的是如何判定投资风险、在规避风险时如何进行投资组合才获取最大的收益。哈里马科维茨在20世纪50年代首次提出投资组合理念，并提出均值方差模型。该理论模型为之后投资组合问题的研究奠定了基础。为了获得更加符合我国市场的投资组合模型，并且结合科学的方法更快更准确地为投资者提供合理的投资组合，本文在经典均值方差模型的基础上，结合我国投资市场现状以及我国投资者的需求主要做了以下几个方面的研究：

(1)基于经典的均值方差模型，提出实用的最优投资组合概念。通过对未来的收益方差进行预测，然后引用均值方差理论计算未来投资的风险，求得风险最小的组合为最优投资组合。

(2)基于最优投资组合的概念，采用统计学方法GARCH模型，以及机器学习方法LSTM模型构建投资组合。首先对选中股票池中的数据进行收益率方差的预测，在此基础上计算具有最小收益率方差的组合构建最优投资组合。

(3)基于最优投资组合的概念，采用图卷积神经网络模型，对股票池中的股票进行收益率方差预测并构造投资组合。首先通过对上证50的股票池中，依据地域板块选中主要三个地域板块的22支股票，进行图构建之后再放入模型，预测熊市牛市以及震荡区间的收益率方差，之后经过计算求得最优权重，构建具有最小收益率方差的最优投资组合。

研究表明: 通过GCN模型构建的最优投资组合、GARCH模型建模的最优投资组合和LSTM模型构建的最优投资组合都可以很好的抵抗市场的风险，在牛市能保证可观的收益。在熊市的时候可以取得不错的收益，在股市震荡区间的时候，三者都可以取得正向的收益。三个模型对比，GCN构建的最优投资组合效果更好一些，无论是在熊市、牛市以及震荡区间。GCN模型构建的最优投资组合同GARCH模型、LSTM模型构建的投资组合相比，都具有更好的抗风险能力，更好的经济效益。

With the improvement of the national economic level, stock investment has gradually entered the public eye. As we all know, stock investment has great risks, and the yet to be perfected regulatory system, investors' herd mentality and malicious behavior will increase the risk of the market. Therefore, for investors, what they are most concerned about is how to determine investment risks and how to make investment portfolios to obtain maximum returns when avoiding risks. Harry Markowitz first proposed the portfolio idea in the 1950s and proposed the mean-variance model. This theoretical model lays the foundation for the subsequent research on portfolio problems. In order to obtain an investment portfolio model that is more in line with the Chinese market, and combine scientific methods to provide investors with a reasonable investment portfolio faster and more accurately, this paper, on the basis of the classic mean variance model, combines the current situation of my country's investment market and the investment situation of Chinese investors. The needs are mainly studied in the following aspects:

(1) Based on the classical mean-variance model, a practical concept of optimal investment portfolio is proposed. By predicting the variance of future returns, and then using the mean variance theory to calculate the risk of future investment, the portfolio with the smallest risk is obtained as the optimal portfolio.

(2) Based on the concept of the optimal investment portfolio, the statistical method GARCH model and the machine learning method LSTM model are used to construct the investment portfolio. Firstly, the data in the selected stock pool is forecasted for the return variance, and on this basis, the optimal portfolio is constructed by calculating the portfolio with the smallest return variance.

(3) Based on the concept of optimal investment portfolio, a graph convolutional neural network model is used to predict the return variance of stocks in the stock pool and construct an investment portfolio. First of all, by selecting 22 stocks in the main three regional sectors from the stock pool of the Shanghai Stock Exchange 50 according to the regional sectors, after constructing the graph, they are put into the model to predict the bear market, bull market and the yield variance of the shock range. The optimal weights are used to construct the optimal portfolio with the smallest return variance.

The research shows that the optimal investment portfolio constructed by the GCN model, the optimal investment portfolio constructed by the GARCH model and the optimal investment portfolio constructed by the LSTM model can well resist the risks of the market, and can guarantee considerable returns in the bull market. In a bear market, you can achieve good returns, and when the stock market fluctuates, all three can achieve positive returns. Comparing the three models, the optimal portfolio constructed by GCN is better, no matter in bear market, bull market and shock range. Compared with the investment portfolio constructed by GARCH model and LSTM model, the optimal investment portfolio constructed by GCN model has better anti-risk ability and better economic benefits.