Abstract Index funds consist of a subset of stocks, an index tracking portfolio, included in the market index. The index tracking portfolio aims to match the performance of the benchmark index. In this paper, we propose a hybrid model for solving the multiperiod index tracking problem, which includes rebalancing concerns, transaction costs, limits on the number of stocks, and diversification by sector, market capitalization, and stock weight. Our hybrid model combines the genetic algorithm (GA) to select stocks of the index tracking portfolio and mixed-integer nonlinear programming (MINLP) to estimate its weights. Finally, we apply our proposed hybrid model to the S&P500 to find an index tracking portfolio that includes those constraints. The results show that our hybrid model is able to create an index fund whose return rate is similar to the market index with significantly lower risk.

中文翻译：

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使用混合模型优化指数基金：遗传算法和混合整数非线性规划

摘要 指数基金由包含在市场指数中的一组股票、一个指数跟踪投资组合组成。指数跟踪投资组合旨在匹配基准指数的表现。在本文中，我们提出了一种解决多期指数跟踪问题的混合模型，其中包括再平衡问题、交易成本、股票数量限制以及按行业、市值和股票权重进行多元化。我们的混合模型结合了遗传算法 (GA) 来选择指数跟踪投资组合的股票和混合整数非线性规划 (MINLP) 来估计其权重。最后，我们将我们提出的混合模型应用于 S&P500，以找到包含这些约束的指数跟踪投资组合。