An actively managed portfolio almost never beats the market in the long term. Thus, many investors often resort to passively managed portfolios whose aim is to follow a certain financial index. The task of building such passive portfolios aiming also to minimize the transaction costs is called Index Tracking (IT), where the goal is to track the index by holding only a small subset of assets in the index. As such, it is an NP-hard problem and becomes unfeasible to solve exactly for indices with more than 100 assets. In this work, we present a novel hybrid simulated annealing method that can efficiently solve the IT problem for large indices and is flexible enough to adapt to financially relevant constraints. By tracking the S&P-500 index between the years 2011 and 2018 we show that our algorithm is capable of finding optimal solutions in the in-sample period of past returns and can be tuned to provide optimal returns in the out-of-sample period of future returns. Finally, we focus on the task of holding an IT portfolio during one year and rebalancing the portfolio every month. Here, our hybrid simulated annealing algorithm is capable of producing financially optimal portfolios already for small subsets of assets and using reasonable computational resources, making it an appropriate tool for financial managers.

中文翻译：

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混合模拟退火算法精确求解索引跟踪问题

从长远来看，积极管理的投资组合几乎永远不会跑赢市场。因此，许多投资者经常求助于被动管理的投资组合，其目的是遵循特定的金融指数。建立这种被动投资组合的任务也旨在最大限度地降低交易成本，称为指数跟踪（IT），其目标是通过仅持有指数中资产的一小部分来跟踪指数。因此，这是一个 NP 难问题，并且无法精确求解超过 100 个资产的指数。在这项工作中，我们提出了一种新颖的混合模拟退火方法，该方法可以有效解决大型指数的 IT 问题，并且足够灵活以适应财务相关的约束。通过跟踪 2011 年至 2018 年之间的 S&P-500 指数，我们表明我们的算法能够在过去回报的样本内找到最佳解决方案，并且可以进行调整以在样本外期间提供最佳回报未来的回报。最后，我们重点关注一年内持有 IT 投资组合并每月重新平衡投资组合的任务。在这里，我们的混合模拟退火算法能够为一小部分资产生成财务上最优的投资组合，并使用合理的计算资源，使其成为财务经理的合适工具。