基于马科维茨投资组合理论的实证研究——以东方财富沪股通市场股票为例
Empirical Research Based on Markowitz Portfolio Theory—A Case Study of Orient Fortune Shanghai Stock Connect Stock Market

随着我国经济的持续增长，投资的队伍也在不断壮大，“鸡蛋不能放在同一个篮子里”是所有投资者都知晓的道理。同时，鸡蛋该如何分配便成了我们所面临的问题。本论文通过应用马科维茨模型，研究并分析了沪股通中的投资组合优化问题。我们收集了沪股通中5只不同行业的股票从2023年12月1日到2024年3月8日之间62个工作日的收盘价为样本数据，首先将股票的日收盘价转换为日收益率，然后根据这些数据运用Matlab计算出了每只股票的期望收益率、方差、协方差矩阵等，并进行了初步分析。其次，我们利用二次规划的拉格朗日乘子法求解出在禁止卖空和允许卖空两种条件下的最优投资组合权重、期望收益率和标准差。实证结果表明，在“允许卖空”条件下，最优投资组合的收益率r_p = 0.11%，投资风险σ_p = 0.007853；在“禁止卖空”条件下，最优投资组合的收益率r_p = 0.15%，投资风险σ_p = 0.00827。由此可见，“禁止卖空”条件下的组合收益率较高，同时所对应的风险(标准差)也较大。
With the continuous growth of China’s economy, the investment team is also constantly expanding. “eggs can not be placed in the same basket” is a truth known to all investors. At the same time, how to allocate eggs has become a problem we are facing. This paper studies and analyzes the investment portfolio optimization problem in the Shanghai-Hong Kong Stock Connect by applying the Markowitz model. We collected the closing prices of 5 stocks from different industries in the Shanghai-Hong Kong Stock Connect as sample data from December 1, 2023 to March 8, 2024, a total of 62 working days. Firstly, we converted the daily closing prices of the stocks into daily returns, and then based on these data, calculated the expected return rate, variance, covariance matrix, etc. of each stock using Matlab and conducted preliminary analysis. Secondly, we used the Lagrange multiplier method of quadratic programming to find the optimal investment portfolio weights, expected return rate, and standard deviation under the conditions of prohibiting short selling and allowing short selling. The empirical results show that under the “allowing short selling” condition, the optimal investment portfolio return rate (r_p) is 0.11% and the investment risk (σ_p) is 0.007853; under the “prohibit short selling” condition, the optimal investment portfolio return rate (r_p) is 0.15% and the investment risk (σ_p) is 0.00827. Therefore, it can be seen that the portfolio return rate under the “prohibit short selling” condition is higher, but the corresponding risk (standard deviation) is also higher.