Abstract: As the Chinese stock market matures and market efficiency continues to improve, the application of statistical arbitrage strategies is growing increasingly. The narrowing profit margin for single-stock pairing strategies poses a challenge to the optimization of traditional pair trading strategies. As China gradually relaxes restrictions on margin trading and introduces short-selling mechanisms, the operational efficiency of the capital market has been significantly enhanced. The rapid development of margin trading and the continuous expansion of target stocks have provided more arbitrage opportunities, indicating substantial potential and application for pair trading strategies in China.
This paper introduces a multi-stock pair trading optimization strategy-the MultiPT optimization strategy, which establishes a flexible framework for pair trading stock selection and expands the research scope of pair trading methods. The proposed optimization algorithm overcomes the limitation of traditional pair trading strategies, which require an equal number of matched pairs, enhancing the flexibility and practicality of stock selection. Based on the minimum distance method and cointegration test idea, the study seeks stock pairs with the minimum price distance, considering non-zero stock weight constraints. It tracks dynamic stock price differentials through cointegration tests to capture arbitrage opportunities in long-term equilibrium relationships. Given the non-linear nature and constraints of the optimization model, the Sequential Quadratic Programming (SQP) algorithm is used effectively to solve the model, finding multiple locally optimal solutions and determining the optimal weight distribution between two sets of stocks to construct the best pair combinations.
The study selects the constituent stocks of the CSI 300 Index and the Wind Industry Index from the Chinese A-share market as back-testing samples, spanning from January 1, 2015, to December 30, 2020. The back-testing results show that, compared to traditional GGR and cointegration strategies, the multi-stock pairs trading model achieved excess returns of at least 15.17% and 14.97% in the CSI 300 constituent stocks and Wind industry samples, demonstrating significant advantages in multi-stock pairing. The study also finds that the MultiPT optimization strategy yields the highest returns with two stocks in the pairs, with strong risk hedging capabilities. However, as the number of stocks in the pairs increases, the stability of the strategy decreases; when the number of stocks reaches a preset limit, despite reduced returns, higher strategy stability will be maintained. This indicates that under certain conditions, increasing stock pairs can help diversify risk, but may reduce returns. Notably, the GGR, cointegration, and MultiPT optimization strategies all perform more prominently during market downturns. Overall, the multi-stock pair trading strategy shows robust performance in various market conditions and samples, consistently outperforming the single pairing algorithms in GGR and cointegration strategies.
The research results confirm the feasibility and effectiveness of the multi-stock pair trading strategy, providing a model, algorithm guidance and empirical validation for pair trading strategies in the Chinese stock market. This study offers detailed evidence for investors to understand and implement pair trading strategies in various market situations, providing theoretical support and practical guidance for exploring stock market vitality and promoting high-quality development in China’s financial market. Future research will design selection rules based on investment preferences and constraints, employing a broader and more diversified dataset to verify the robustness and effectiveness of the multi-stock pair optimization algorithm.

Key words: multi-stock pairs trading, SQP method, minimum distance method, cointegration test

摘要： 随着中国股票市场的日益成熟与市场效率的持续提升,统计套利策略的应用日益增加。单支股票的配对策略盈利空间收窄,传统交易策略面临着性能优化的挑战。针对此问题,本文提出了一种多支股票配对的交易优化策略—MultiPT优化策略。首先基于最小距离法和协整检验思想构建配对选股模型,随后通过序列二次规划算法对优化模型求解,以确定两组股票的最佳配对组合。本研究选取中国A股市场中的代表性样本数据进行回测。实证结果显示,相较于传统GGR和协整策略,MultiPT优化策略在沪深300指数成分股和Wind分行业样本中分别实现了至少15.17%和14.97%的超额收益,显示出多支股票配对的显著优势。此外,配对股票数量与风险水平呈正相关关系。值得注意的是,GGR、协整以及MultiPT优化策略均在市场低迷时期表现更为突出。实证结果验证了MultiPT优化策略的可行性和有效性,为探索股票市场活力、推动中国金融市场的高质量发展提供理论支撑和实践指导。

关键词: 多支股票配对交易, SQP算法, 最小距离法, 协整检验