A new investment method for statistical arbitrage using eigendecomposition to generate stationarity

This study proposes a new method for constructing statistical arbitrage strategies. Statistical arbitrage is an investment strategy derived from arbitrage. Both strategies exploit distortions between asset prices, but they differ in that arbitrage assumes a deterministic adjustment of distortions between asset prices. In contrast, statistical arbitrage assumes a stochastic adjustment of distortions. Therefore, stable operability is a crucial issue for statistical arbitrage. However, methods based on cointegration tests, which previous studies have often used for statistical arbitrage, do not necessarily allow for the construction of stable portfolios. The main objective of this study is to overcome such problems. Specifically, we plan to use eigendecomposition to find stable portfolio components and improve the profitability and stability of portfolios using standard deep learning architectures such as Gated Recurrent Unit (GRU) and Convolutional Neural Network (CNN). Through numerical simulations using a dataset of stocks listed in the S&P 500, we first demonstrate the superiority of our method over conventional methods based on cointegration tests. Then, we verify that we can improve the method’s performance with the help of deep learning.