Abstract
We study a systematic approach to a popular Statistical Arbitrage technique: Pairs Trading. Instead of relying on two highly correlated assets, we replace the second asset with a replication of the first using risk factor representations. These factors are obtained through Principal Components Analysis (PCA), exchange traded funds (ETFs), and, as our main contribution, Long Short Term Memory networks (LSTMs). Residuals between the main asset and its replication are examined for mean reversion properties, and trading signals are generated for sufficiently fast mean reverting portfolios. Beyond introducing a deep learning based replication method, we adapt the framework of Avellaneda and Lee (2008) to the Polish market. Accordingly, components of WIG20, mWIG40, and selected sector indices replace the original S&P500 universe, and market parameters such as the risk free rate and transaction costs are updated to reflect local conditions. We outline the full strategy pipeline: risk factor construction, residual modeling via the Ornstein Uhlenbeck process, and signal generation. Each replication technique is described together with its practical implementation. Strategy performance is evaluated over two periods: 2017-2019 and the recessive year 2020. All methods yield profits in 2017-2019, with PCA achieving roughly 20 percent cumulative return and an annualized Sharpe ratio of up to 2.63. Despite multiple adaptations, our conclusions remain consistent with those of the original paper. During the COVID-19 recession, only the ETF based approach remains profitable (about 5 percent annual return), while PCA and LSTM methods underperform. LSTM results, although negative, are promising and indicate potential for future optimization.
Abstract (translated)
我们研究了一种流行统计套利技术——配对交易的系统方法。不同于依赖于两个高度相关的资产，我们将第二个资产替换为使用风险因子表示法复制第一个资产。这些因素是通过主成分分析（PCA）、交易所交易基金（ETFs）以及我们的主要贡献——长期短期记忆网络（LSTMs）获得的。我们检查主要资产与其复制版本之间的残差是否具有均值回归特性，并为此类足够快速地呈现均值回归特性的投资组合生成交易信号。 除了介绍一种基于深度学习的复制方法外，我们将 Avellaneda 和 Lee (2008) 的框架适应于波兰市场。相应地，WIG20、mWIG40 以及选定的行业指数替换了原始的 S&P500 投资组合，并且风险无风险利率和交易成本等市场参数更新以反映当地条件。我们概述了整个策略流程：风险管理因素构建、通过奥恩斯坦-乌伦贝克过程对残差进行建模，及信号生成。每种复制技术及其实际应用都得到了描述。 策略性能在两个时期进行了评估：2017年至2019年和经济衰退期的2020年。所有方法均在 2017-2019 年期间获利，其中 PCA 实现了大约 20% 的累积回报，并且年度化夏普比率达到 2.63 左右。尽管进行了多次调整，我们的结论仍与原论文保持一致。然而，在新冠疫情期间，只有基于 ETF 方法仍然有利可图（年回报率约为5%），而 PCA 和 LSTM 方法表现不佳。虽然 LSTM 的结果是负的，但显示了未来优化的巨大潜力。
URL
https://arxiv.org/abs/2512.02037
