关键词: 多支股票配对交易, SQP算法, 最小距离法, 协整检验

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